this thread is getting a bit too theoretical/semantical, is it not? making one big metal enclosure around separate enclosed components and calling it a receiver because it still has one power cord? that's fine, i guess. it would be TOTL if it used TOTL components, and it would obviously compete with any components separately for the same reasons. but nobody's done that that i know of, so it's essentially moot w.r.t. the OP.
let's say you call the SX-1980 the most TOTL receiver of all time. for the cost of the average of the last couple eBay sales, you could get an EW'd Spec 2 amp, a Spec 1 preamp, and still have around $400 to spend on the tuner of your choice, which may or may not beat the 1980's, IDK. i admit, it's handy to have everything in one box that takes up less vertical space, and it may look cooler, but i feel pretty confident about which setup would perform better. maybe i'm missing the point, though.
and we've definitely gotten off topic from "Integrateds vs TOTL receivers." strictly on that note, i'll say that i've always figured that most companies' TOTL integrated was just a slightly better laid out version of their TOTL receiver.
The point is, when doing a comparison, one must compare individual units. It is no use saying integrated amplifiers are better than receivers, because some receivers are better than some integrated amplifiers, and vice versa. If we confine this to TOTL units, whose line are we talking about, and from what time period? If we are including all brands and all times, we will find quite a variety of quality involved in both, and we will have some TOTL receivers being better than some TOTL integrated amplifiers, and vice versa.
The same applies to getting a separate preamp and power amp(s).
As a matter of fact, some receivers have been very well made, being better than quite a few separates. Simply counting the boxes is no way to determine quality. The fact that some people are prejudiced against receivers explains why so many low end separates have been made over the years, as they appeal to people who can't afford the best and are deluded into believing that receivers cannot be good. But they would be well advised to get over their prejudice, and buy a good receiver instead of low end separates.
The bottom line is this: When selecting a particular component, the number of boxes the stuff is in is not what determines the quality. It would be extremely foolish to pass up a well made receiver for poorly made low end separates.
Again, as a matter of fact, the very best components ever made have been separates, but that is simply because that is the way manufacturers have chosen to do it. They could, if they wished, put those same circuits in a receiver, though, of course, it would end up being a very large receiver. Of course, the very best equipment ever made is totally irrelevant to most people, as most people cannot afford it. The reality is, one needs to consider what is the best one can afford, and what that will end up being is, in many cases, a receiver, though in other cases it would end up being separates.
Of course, once one is in the used market, what will be the best value will depend upon the deals one encounters, which may go against the general trend.
Going with your particular example of a Pioneer SX-1980 at typical used prices, I agree that it is not a good value compared with some other options. Too many people recognize it and value it too highly for it to be normally a good buy.