Always fun to re-visit this subject.
https://www.stereophile.com/content/carver-challenge
https://www.bobcarvercorp.com/carver-challenge
I think that there is a "tube sound", it isn't intentional nor more pure, and it can be duplicated.
In amplifiers, it is my opinion and experience that many SS amplifiers don't do low output well, just the nature of the solid-state devices' linearity at very low switching voltages and why Class A was the standard for so long, but new SS devices and feedback schemes have improved that "first watt" SQ a great deal in SS, it was more natural for a tube to produce.
In instruments like a guitar amp, I don't think that the type of distortion that a tube produces when it is over-driven has been perfectly emulated in SS amplifiers. That distortion is important to Guitar guys and the like and might be part of why the mistique still exists in audio. In stereo systems the nature of the tubes to compress/collapse more when overdriven vs solid-state's ability to create HF distortion and more tweeter damage used to make them seem safer to some, but Powerguard and other protection that is in quality amplifiers starting in the '70s has really removed that excuse for favoring tubes as well.
I have some tube sets, and some SS sets, as
@twiiii mentions there was a change in the quality of available replacement tubes beginning in the '70s, which I believe that at least one of my vintage tube sets doesn't tolerate well. I also feel that my modern tube sets don't really care whether it's running a $$$ NOS RCA Black-Plate or a new Svetlana/New-Sensor output tube.
I believe that the "tube sound" in my vintage tube sets was simply the sound and voicing that came from the design of those amplifiers in their time, with the available knowledge, measurement equipment, and amplification devices. Similarly many here (including me) feel that some of the older SS devices have a lot of "tube warmth", examples being the MC2505 & MC2105, I feel that they have a different voice than for example the next generations of SS from McIntosh. Intentional? I don't think so, it's just the most accurate that could be produced at the time, hell they didn't even have PNP devices in the outputs of the 2505 & 2505-2, geranium transistors through the early versions of the 2105 also eventually gave way to the more modern silicon devices, which continued to evolve. VIntage gear sounds different.
The newest generation of amplifiers and preamps from McIntosh certainly are voiced to whatever McIntosh feels that their market wants, regardless of the devices used inside. I believe that if Bob Carver could replicate "any" amplifier's sound in a couple of days in a motel room, McIntosh can in their well-equipped Engineering department also duplicate any sound that they want to for their new amplifiers. If it sounds "tube-like", it is because McIntosh management wants it that way. Most likely their new tube amps and preamps are designed to sound a particular way.
If you like the sound of a particular piece, be it vintage or new, that's the one you want. Whether it has tubes or not should not IMO be the reason that you choose it unless you just like looking at glowing glass bottles (I do), in which case it's the asthetics adding to your music experience, which is a good thing too. I feel that most of the vintage audio has its own sound, you can try a C26 or MC2505 if you want warm as much as you can choose a C2700, I'm willing to bet you will hear more "warmth" from a propely serviced 2505 than most any new tube set.
JMO, and I spent a lot of time at the last AXPONA trying to find the line between new tubes and new SS and pick out a new system, could hear as much warmth in some new esoteric SS as other new tube gear. Speakers tended to make much more difference to me.
Kind of like vinyl vs digital, there are fans and fanatics, won't ever be agreement on which is best.