Good Question. Profile is supposed to match media type, bu I know what you  mean. Let's say I am all set to print and, whoops, I want Luster paper. I change and the size paper  changes to the last time. I have to redo orientation and sometime size. I make printer setups for 5 x 7, 8 x 10,, 13 x 19, in horizontal and vertical if it is a media I use often.
But let's wait for Mike. He usually has a button I forgot.
Stay well
Fred

Funny - your final phrase "unless the new media type has a smaller page size associated with it." is the one that bit me. I recalled an old 11x17 luster print job but now wanted to print on matte. But the last time I used the Hot Press Natural media type was on letter size paper. So as soon as I changed the media type, of course, I received the freehand placement warning and then had to reassemble the layout. What was nice is that even though it muffed up the size, it pulled up the correct profile, which otherwise I would have had to hunt for as it is a rather obscure file name. This is all easy enough to manage; it did cost me at least 45 seconds of extra work. Just wanted to know that I wasn't doing something wrong; sounds like it's working as it should even though I would like to be able to change media type without it changing the size.

Yep - that's really what I normally do. And that's the best and right approach.  My bad in that I stumbled over this box of Hot Press Natural which (why did I buy it in the first place?) I can't even remember when I last used. So had no setup (I do now). Also trying my best to destroy the printer so that I can buy that bottle ink printer.