Here's my educated guess on this. When the park opened, Walt wanted the Mouseketeers to entertain regularly, which they did for the first summer.
When they finally hit the studio to do the daily TV show, it was realized that the entertainment was a nice touch, so they continued on with a troupe called the "Kids."
I think that the reason they were called "kids" was the same reason that the Beach Boys weren't called the Beach "Men."
I once had my hand on "The Kids of the Kingdom" 1968 LP at a record show, but didn't buy it because the vendor also had the "Hall of Presidents" LP for $12, and at the time I couldn't afford both. (I think he wanted $20 for it, but I was young and poor!)
I don't really lose sleep anymore over this music, because little by little we're getting crisp digital copies of everything now. If everything was available at once, that wouldn't be any fun, would it?
P.S. Danny, I think I may have something to trade with you finally. (Not MSEP related, but cool just the same.)