As far as I have ever understood, multi-coating improves a number of characteristics, but the fact that it appeared around the same time as the surge in colour film use is merely coincidental. Single coated and uncoated lenses usually work equally well - or poorly - with panchromatic black and white film and normal colour colour film. And any colour cast imparted by yellowing of the lens can probably be filtered out if your intention is to shoot slide film.
Newer cameras are more likely to have multi-coated lenses, so that relative "newness" may be a good reason for that criteria. Of course, that may affect one of the other specified criteria - affordability.
I'm fond of TLRs, and would recommend them. I don't know whether my 6x6 Baby Bessa is sporting a multi-coated lens, but I like it too.