NFL ratings would go down if they played on Saturdays because a large enough chunk of college fans are more emotionally invested in their college than pro team. They took over Thursday because it only had a couple of college games. When you have the full college slate, they're going to take a hit, and the last thing they'd want to do is make a move that made this dominant product seem less, well, dominant.
Maybe incrementally, but not by that much. The casual viewers by and large will always opt to watch an NFL game over a CFB game.
So, you’d lose the die-hard fans of CFB teams playing, but any casuals would still watch the NFL product.
I could see the NFL wanting to do it because you’re increasing exposure. IE, rather than 4-5 games sharing a time slot on Sunday and the audience segmented regionally, you add one or two nationally televised games on Saturday where your only competition is CFB.
I could see the networks (or certainly a streamer) wanting it because you can trade a game that would fetch maybe 5-6M, with a game that would conservatively fetch 10M and likely much more.
Literally, the only thing I think stopping this is that anti-trust law, not worry about TV ratings. When CFB doesn’t play later in the year, the NFL immediately puts 2-3 games on Saturday