I will post a few thoughts, then I will go away and let you folks hash this out however you wish:
If you remove the main caps from your amp and power it up, you will let the magic smoke out, pretty much immediately. You can ignore me and try it, but, you have been warned.
The current that is going to the load is NOT coming out of the transformer directly. The only time that the transformer is sourcing current is when the transformer output voltage exceeds the charge on the caps + the voltage drop across the rectifier(s). The main supply caps are the reservoir supplying the current to the load (well over 95% of the time), hence, are in series with it. If you look at a plot of the current coming out of the transformer, once the main caps are charged, what you will see is large, short spikes, with very high ramp rates, that are limited by the transformer inductance and series resistance, as well as by the ESR of the caps. These spikes occur only at the peaks of the transformer half-cycles. At any other time the only place the outputs get current from is from the main caps.
If the caps were supplying a completely passive circuit (no active components: diodes, transistors, FETs, etc.), then the capacitive reactance of the caps would play major roles, as would their parasitics (ESR, inductance, shunt capacitance, etc.). Capacitors are probably one of the most complex and least ideal components in the electronics world. They are very hard to model accurately, from cap design to cap design. They are also quite unstable (operating characteristics moving all over the place with time, temperature, applied voltage, etc.). However, the caps are not supplying a passive circuit, but a complex (mathematically), active circuit.
Most commercial power amps (since this is what is under discussion here) of the day (not modern switchers, but analog/linears) utilize feedback from the output back to the input. They are essentially closed-loop servos, where the input voltage dictates the output signal (current or voltage, dependant upon the design). This results in the truth of
EW's original statement: "The quality of the output signal is primarily dependant upon the amp topology, not upon the capacitors used" (sorry if I failed to get the essence). Whatever non-linearities, caused by various components of the servo (including and especially, coupling and filter caps), regardless of the source of those non-linearities, will be compensated for by the servo, up to the point where the servo's response hits a limit (frequency response, phase linearity, transient response, etc.). With a specific, instantantaneous, input voltage, a specific, instantaneous, current or voltage is to be present at the output. If the output does not match the input dictation (point in time by point in time), the servo pulls or pushes to make it so. Part of the magic in servo design is to make the phase linearity flat across the required frequency range of the servo, so that the delay from dictation to output is flat, for us, across the audio spectrum (plus a bit, for spec derating). If your servo can't handle a little bit of variation in capacitor response, you need to get out of the business, or you will destroy the reputation of your company. The better the "design" (not the parts), the better the response. The "magic" is in the ability to design a servo that does not need expensive parts to produce an expensive sounding result.
If you analyze any of the significant amps of the day, you will see that they did "not" use esoteric, magic, TOTL parts (anywhere). They did use parts that were optimized for audio, but they were not magic or expensive (relative to what might have been available then, or even today). As a matter of fact, modern power transistors are so much better (frequency response-wise) that you actually have to slow them down a bit to use them (in some cases) in the old power amps, or the servos will go unstable and oscillate. That is with "better" parts, in almost every respect, to the originals.
Keep this in consideration: The amps were designed for the parts they used, and the designs were balanced to maximize performance and profit, while minimizing cost and maufacturing complexity and difficulty. The balance is not an electronically delicate balance, but a financially delicate balance. Audio band servos are not hard to design so that they are not teetering on the edge of response degradation. To maintain the name, you must derate your designs a bit, so that as things age, the device still works up to spec, for a calculated life time of the product (anticipated end of life and predicted parameter drift of capacitors included in the calculation). What this means is that, you want the design to have enough performance headroom to be able to compensate for component aging and other time-related changes and other dynamics, related to operating conditions, without loss of peformance.
If someone replaces old filter caps with new, and the sound suffers, there is something wrong with the servo. What should have happened is, the performance headroom of the servo should have been been restored, or at least increased, back in the original factory direction, and the individual non-linear contributions of the aged parts should have retreated back under the cover of servo compensation. You simply have more troubleshooting work to do, that is all. Test me in this:
Give the Sansui amp in question, with the new and old caps, to EW and turn him loose. If the amp does not sound sweeter with the new caps, when EW is done with it, I'll eat my hat. He knows power amp servo circuits probably better than anyone on this board, and most audio techs in the country for that matter.
Sansui (Pioneer, Harmon Kardon, Phase Linear, et. al) did not listen to main filter caps and pick the most appealing. I promise you that what they listened to were designs, and topologies. If you can hear the difference between main filter caps with a particular power amp design, the designer would have been sent back to the drawing board. I am a design engineer with over 25 years of experience in design for manufacturing. I know a little bit about what I am taking about.
Folks, what has been stated before is the fact. Argue with physics, or with each other, if you wish. However, it will not change the physics: "A properly designed audio power amp should be as close to a wire with gain as possible" If you want color in your music, that is a completely different topic, as to what color appeals best to the ear. In my opinion, color, if any, is the business of the audio transducers (speakers or headphones). You can't polish a horse apple. If the design stinks, you won't improve it much with esoteric caps. A good design can tolerate inexpensive caps, if not, it is "not" a good design.
I am frequently complemented in how much better I have made a piece of equipment sound. I am not in the business of mod'ing gear. I will do it, if requested, but I will resist, and sometimes refer the work to others. I use better quality parts in my recapping and restoring, but not in anticipation of improved sound, but of increased life for the gear. Essentially, I don't improve the sound over what was originally there. I simply "restore" it, to what it was originally. If it wasn't very good from the factory, it won't be very good when I'm done with it. Now, sometimes you can improve the performance of a piece of gear, but that requires modification of the "design." Basic cap substitution, except in certain critical points, is not a design mod. Simple mods, like better op amps in the input current mirrors, etc, can be done, and will improve performance over that from the factory. But, what I do normally is to put in, for example, better caps, with longer life, better ability to tolerate heat, etc. This doesn't improve the sonics all that much, but does make the piece of vintage gear more reliable, long term. "If it ain't broke, don't fix it" is a nice platitude, however, I say, "If you want to significantly increase the likelihood that your amp will be singing for many more years, you better recap it." Otherwise, "You pays your money, and you takes your chances." I just lost my bench amp (a beautiful, Pioneer SPEC-4) due to bad main power supply caps. If I had gone in and recapped the unit, in the first place, it would have cost me the $125 for the 4 big caps, + whatever the rest of the caps cost, and labor, rather than now having to replace almost every semiconductor in the box.
There are 3 ways to get wisdom:
1) straight from the source (mfg data sheets and manuals, etc.)
2) you can get it from someone who got it way number 3
3) the hard way.
The bottom line is this: Aluminum electrolytics depend upon a "moist" electrolyte paste to function. The aluminum electrolytic is then greatly dependent upon the seal of the cap can to retain the electrolyte. The electrolyte actually ages, and changes as well as dries. No seal is perfect. Some are better than others, even in a particular production run of a single cap model. Hence, a large percentage of vintage gear is still working. Heck, there is still an original Edison incandescent light bulb burning in a firehouse somewhere back east. But that means that the individual part has greatly exceeded its anticipated EOL (end of life). EOL is not a prediction of when all the parts will fail, but a prediction of when you can anticipate them to begin to drop out (some sooner, some later, some much later, hopefully most, much later). You know what? I bet that no-one would be a bit surprised if that bulb burned out this afternoon. It has had a real good run. Neither should you be surprised if your prized piece of vintage gear releases some of its magic smoke, right in the middle of showing it off to your sceptical young nephew. Whoops

Cest la vie
I now give up. You folks go ahead and go at it, if you wish.
Enjoy,
Rich P