A more likely scenario is that we'd be supporting allies in those theaters, not fighting united continent-blocs. Either way, you can't fight across an ocean without lots and lots of cargo ships.
> If we're talking about US/European allies vs China - then European allies have the ships and capacity to build more.
Not necessarily enough capacity if you're losing tens of ships a month, and there's no guarantee those would remain intact, or that we'd even be on the same side. It's easy to assume stable, decent-enough, friendly governments will continue to be that way indefinitely, but they may not (for other actors, it's very much worth worrying whether the US will remain so, for instance)
> You have to give a concrete example where US would need to have a merchant fleet, where allies aren't willing to provide.
We literally have a real world example, which is far more valuable than made-up scenarios, that was arguably won primarily by US industrial capacity and the ships to direct that output to the right places, and it's still (barely, admittedly) within living memory. Among the most famous machines of that war is a class of merchant ship, for very good reason.
Unless we suppose that modern great-powers wars will be over so fast that shipping wouldn't have time to play a major role, or we think that anti-shipping weapons would be so effective and have such wide reach that no amount of shipping & protection could keep a meaningful proportion of a shipping fleet afloat for any useful length of time even if we started with a significant upper-hand overall—and I sure wouldn't want to bet on either of those things—it seems like that'd still be highly relevant in any major conflict in, at least, the near- to mid-term future.