No, the neck was 'under the radar' back in the day - guys just played the neck that was on the sax they tried and liked. If something happened to the neck, they would get a factory replacement. Obviously, somebody somewhere was swapping necks to find better combinations but this didn't 'go viral' until a few years after SOTW started.
The tenor not only has the largest neck of the saxes, it also has the largest volume (water capacity) of the sax necks, plus it is the largest neck in relation to the rest of the sax. It also has the compound curve. These attributes mean there are many more variables in a tenor neck than sop, alt or bar, so there are very real differences in necks that look alike. Necks made at the same place to the same design can play differently. Selmer and probably other manufacturers knew this and it is known that Selmer USA did swap MK VI tenor necks around during final adjustment/play-testing to create better combos.
Being longer, there is more of a 'bending moment' associated with the main arch which is the part that flattens in a 'pull-down' than the other saxes. I have the original neck with my 186xxx MK VI tenor and I am not a player who pulls necks down - however, it turned out that the neck was damaged to some extent when I received it. I had been playing a Series III Sterling neck on it for years which is an excellent neck, but I never was really satisfied with the horn. I had what was supposed to be a premium overhaul on it but ended up working on it myself for a long time to get the tone/playability back. During that period, I sent the neck to Kim Bock of KB Sax in NYC to see if he thought it needed anything. While it didn't look bad, it turned out the major part of it was more oval than round, and the mouthpipe was too open. I got the neck back and tooted a few notes, but I wasn't finished with the sax yet and I didn't really see any difference. However, once I did fix all the crazy leaks and action problems, I took the neck to a shop about an hour away to have the tenon tightened up to the horn. The next time I played this horn I fell out! The more I played it, the better I liked it. Altissimo does take a little more effort than the silver neck but restoring that original neck is really making the horn pop. The more I get used to it, the better it is. Now I don't like the silver neck and brass III neck on the VI but they are still great on my USA tenor for which the original neck was so awful (it was in perfect physical and cosmetic condition, just a crummy neck) that unless I had found a Paris neck to play on it, I would not have been able to use it.
I've always like Sterling silver necks - my first tenor was a Super 20 with silver neck, made when I was about 5 years old. I got it when I was 16. I've always thought that was what started me on the silver necks. Anyway, I tried one on my baritone, and it really didn't make much difference - I liked the original brass neck better. I guess this is because the baritone neck is the smallest in relation to the size of the whole instrument (I don't know about the bass, contrabass, etc. - this is just about sop, alt, ten, bar) so the neck can make the least difference, all things being equal.
Sorry about the sermon but I have learned a few things about necks over the years and after all, you did ask. You were right, the tenor is the king of the neck swap, and the reasons are as I stated, plus the propensity for the tenor neck to be damaged.