The situation at other airports may be different, but here's a look at possible effects of US's demise using SDF as an example. US now serves SDF from:
plus ORD 6x on UAX codeshare
with all flights on RJs.
DL serves SDF with 5x mainline plus 2x RJ service from ATL. My guess is that DL would upgauge the RJ flights to mainline as a result of US's departure from CLT.
CO serves SDF with 3x RJ service to EWR. Expect frequency to increase plus a possible upgauge to mainline for some flights as a result of LGA and to a lesser extent PHL.
Expect UA to start serving SDF from IAD in (addition to ORD) to cover DCA and some of the PHL traffic. My guess is 5x or 6x RJ service.