If certain technical conjectures are proved, then “V=ultimate L” is an attractive axiom.

The paper “Gödel’s program“, available on my webpage, gives an argument for that. I would guess the technical conjectures are true; in any case, large cardinals should decide them.

“V = Ultimate L” implies CH.

I don’t think we should care how hard it is to understand the statement of “V = Ultimate L”. But in fact, one semester of graduate set theory is all you need to understand it. The conjectures are just that it implies GCH, and is consistent with the existence of supercompacts. One graduate semester is enough to understand the conjectures.

Best,

John