I think the Big 3 first have to figure out exactly how they want to maintain regional feed first. If they continue business as usual, then I think you're exactly right, which is why some ULCCs have already established relationships with University Aviation programs that pump out 1,000 hour R-ATP students. To your other point, plenty of ULCC pilots (to include a 10 year CA) in my Legacy new hire class.

If they figure something else out, be that expanding downwards into 100 ish seat AC (220, etc), or staple, or whatever, then the Legacies will be the place to go for those same students, plus whatever ULCC pilots make the switch.

It's a crazy world out there.