It’s a terrible design for anything else, because it can barely get beyond LEO without in-orbit refuelling.
None of the competing rockets (e.g. New Glenn) resemble Starship in the slightest, because none of them are intended to fly to Mars.
Given SpaceX's business, it seems safe to assume that Starlink was a design goal with at least a similar priority to the Mars goal.
Another use case it'd work fabulous for would be a LEO space hotel business.
Finally, it's also a great rocket for any use case that involves returning large masses, even if the return is from higher than LEO. Yes, it'll be a thirsty beast requiring many refuelling trips, but the tyranny of the rocket equation makes it hard to do any better. If you want to return dozens of tons from the moon or elsewhere you'd be hard pressed to do better than Starship.
Then again, Musk is also big on reusing components as much as possible, so he might have opposed multiple fuels on principle.
You need much larger tanks, so the mass advantage is pretty much completely eliminated. Hydrogen engines generally have much lower thrust for a given size too. Falcon9 or Starship style staging is infeasible with a hydrogen second stage. Rockets that use hydrogen for their second stage separate a lot higher and faster than Falcon9/Starship to make up for this reduced thrust. This makes Falcon/Starship style 1st stage recovery impossible.
Hydrogen would be great for a 3rd stage. If you want it to be recoverable, design a third stage that fits within the Starship enclosure. This would be a fabulous way to do small BEO missions without requiring a whole bunch of refueling.
For most purposes the customer does not care one iota about the booster, they are interested in the cost per kg to get where they are going. For low orbit hydrolox imposes more handling nightmare costs than it saves in amount of rocket, it is not the fuel of choice unless you're trying to impress.
(Now, things change considerably when you looking at deep space. But methalox or even kerolox fueled in orbit still beats hydrolox fueled on the ground. And hydrolox is much less storable--your rocket costs weight, necessary to reach orbit but once you're up there a smaller engine means less wasted mass. The only advantage to a bigger engine is Oberth and that is only truly relevant if you either care about time (Apollo took an inefficient path for this reason), or because you are going to carry velocity into deep space. Look at the flight path of the Webb. The booster flew higher than the maximum efficiency path because the deep space stage was puny. It wasn't powerful enough to circularize normally, the telescope fell back quite a bit before the engine had built up enough velocity to stay up. But it was worth wasting some energy on that in order to not lift as much engine away from the Earth.)
