Couple of points of order.
1. Neither QEC or PoW will complete with a ski-jump. That's quite easy to remove from the design. It is not so easy (at this stage of QEC build) to install EMALS.
2. F35B does not have two engines. It has a shaft driven lift fan.
3. Hawkeye has not been "ski-jumped" in the STOVL sense. Many years ago, Pax River or NAWC Lakehurst (forget which) experimented with a small (<3 deg as opposed to the 12 deg ramps on UK/SP & IT ships) ramp at the end of the cat run to instill an initial climb attitude and AoA - principally with F/A18s. The French may well have run some trials with a similar small ramp (on Foch I think) during the Rafale development, which may also have had one of their Hawkeyes run over it.
4. Andyy has pretty much nailed it wrt the STOVL version. Apart from locking us into a one-horse race for the aircraft (no other credible STOVL jets are anywhere near serious development) and hence major risk, it also led to some utterly barking ideas on recovery techniques. Including one that still gives me nightmares for a number of reasons, although thankfully I don't believe I will ever have to follow-up on the principal one!