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.