I agree with most everything John says above - surely, whatever fave you have if it involves a 1960s Lady Kenmore, it may be due to unique and inspired styling, and an un-matched zeal for glamour and product acceptance from Kenmore's designers.
That said, I agree yet at the same time disagree with the synopsis of the black panel machines and even of Maytag's 1980s models. Right in the middle of the black panel tenure, Sears (according to several of their catalogs) outsold WP, GE, and Maytag combined. We don't have to like these machines for whatever reason, but the buying public sure did, and in enormous and increasing numbers, so what we think today ultimately really doesn't matter. Sears clearly had what buyers wanted at the time, and by the late 70s, there were many other choices besides Sears.
There have been a lot of articles written discussing how Cadillac made a monumental marketing blunder with the Cimarron (the Cavalier clone) but never have I read that Kenmore or Maytag made any sort of foo-pas with their later 1970s or 1980s consoles.
Appliances were becoming unitary non-emotional purchases in a mature market by the mid 1970s, bought on price and reputation. They were not the joyous, high-gloss purchases that they had been when the market was developing in the 1950s and 1960s. We AW.ORGers see all laundry appliances from a much different perspective than does the general consumer/buying public.
There is NO doubt that the 1976 black panel Lady Kenmore was a far cry from the imaginative, sometimes whimsical (and costly) styling that Kenmore employed ten years earlier. Considering that the 1974 Lady K was a styling carry-over from the late 60s, the dramatic and permanent switch from fancy to not-so-much happened with exactly one model. Boom, done...the Lady K was rather homogenized from that point forward until gone a little more than a decade later.
Many people could not look at a 1976 Lady Kenmore in their neighbor's laundry and know that they had a top-end unit. This was not the case in the 1960s. There was not much to distinguish the 1976 Lady Kenmore from the rest of the line either, other than an automatic soak advance (big deal!) and a second rinse. I suspect a lot of customers wrote those features off as stuff they didn't need or have to have, and it stayed that way for many years.
I think that is why we see FAR FEWER of these, relatively speaking, as a percentage of the total line sales, than we did in the 1960s. The time had come and gone for glitzy washers -- they were just too expensive to make and sell profitably.
I guess for us washer collectors, that just gives us reason to collect and save the 60s models, unless you like the newer stuff for many varied other reasons!
G