Would that be a better world than we have now, though, if Chrome was nominally separate from Google but still only exists because Google pays for it? It seems like the same thing with extra steps.
If Chrome cannot be owned by Google (nor Alphabet) then that is an important separation. It means Chrome could auction off the rights. Much as Firefox offers non-Google search in certain markets, which happened in the US at least once.
I believe the default search payments are also part of the antitrust case, so likely those payments will also become illegal, also affecting Firefox and Apple/Safari.