No., a ski jump is not enough for the F-35C.What is political is the senseless restriction placed on the USMC, effectively banning them from putting ski jumps on their LHDs, because to do that would effectively turn those LHDs into pretty cost effective mini-carriers, which the USN fears might become a threat to their big and expensive flat tops.
If the marines were allowed to have ski jumps or even catapults on their LHDs, I think they would have been happy to do away without VTOL altogether and just use F35Cs.
The Harrier and F35B are aircraft with unique capabilities and undeniable cool factor. But aside from landings and take-offs, it's VTOL capabilities is of extremely limited operational utility
If China wants a fixed wing fastjet capacity on their future LHDs, the far easier and more sensible approach would be to add ski jumps or catapults to them rather than go down the VTOL route.
In order to land they would have had to put arrestor cables on. Then since it is a straight deck, there would have been a natural desire for even a mildly angled deck.
None of that is going to happen.
Those vessels and their Harrier combo have fulfilled their mission for decades now. The F-35B will be an even better solution without the need to completely revamp the vessels.