> Hydrogen has better ISP, so your mass budget isn't so tight.
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.
How are you distinguishing Falcon/Starship style recovery? Blue Origin actually attempted first-stage propulsive recovery with their first orbital test, with a hydrogen second stage. (It didn't work, but neither did SpaceX's first attempt.)
Then again, Musk is also big on reusing components as much as possible, so he might have opposed multiple fuels on principle.