The Republicans absolutely don't have an incentive to contest every single House seat (neither do the Democrats), and they don't. For instance, 2 cycles ago, an avowed neo-Nazi --- who literally stood on Chicago street corners in a Nazi uniform with a bullhorn --- took the GOP nomination for Lipinski's seat. That was possible because, at the time, running as a Republican against Lipinski was suicidal. The GOP did not contest that seat.
Each cycle, both parties make red-to-blue and blue-to-red lists of districts to flip, and allocate money disproportionately to them.
Even setting aside top-down party decisions, which clearly happen, seats aren't contested seriously for knock-on reasons: the best candidates won't run for hopeless seats, because the loss taints them and opens them up to carpetbagging charges when they try to contest other districts.
I don't think I disagree with your whole analysis, but the argument that "Republicans have an incentive to contest every single House seat" clearly doesn't hold.