What I wonder is whether United could attempt Frankfurt to...

Honolulu.

As best I can tell, there is no nonstop service from Europe to Hawaii. I realize that Hawaii's tourism is overwhelmingly Japanese and American, with a growing Korean contingent, but I really doubt there's insufficient interest from Europeans to make it work. Furthermore, starting a nonstop could substantially drive demand.

The 789 is probably the largest plane that could regularly run a profitable 3x weekly service. But I think it could be marketed effectively. Plus, HNL is essentially a UA focus city with international service (HNL-NRT), so the operational infrastructure exists to handle the flight, which reduces the risk of testing the route. At 7450 miles, FRA-HNL is also 1000 miles shorter than the SFO-SIN route United was operating pre-pandemic.

I suppose the obvious European alternative is LHR (no, I don't mean political Europe), which United could also do given its London presence. But LH at FRA would provide the necessary intra-European connections.