Two things don’t make sense to me regarding Kenmore’s cool down protocol:
1959-1960 models (had a ‘59 LK and grew up with a ‘60 Model 80) did several partial drains and refills with no agitation whatsoever. I used the Wash ‘n’ Wear Sturdy cycle for fun a couple of times, which provided medium temp wash water (warmer than warm, but not outright hot). After all those refills—don’t recall how many anymore, but I’d guess it was 4 or 5—the water at the front of the tub was still not cold. The water in the rear half of the tub, where the fresh water rained in, was, of course, cold.
Fast forward a number of years and it started agitating as soon as the refill began. So you’ve gone to all the trouble of treating your W ‘n’ W items carefully, only to have them jerked around by (albeit slow) agitation with only half a tub of water.
Why didn’t they let the machine agitate for a bit once each refill was complete? There would be no warm spots and it would be gentler to fabrics.