H bombs don’t use tritium for their main fusion stage. Even Castle Bravo used Lithium-6. Tritium was used in initiators to increase neutron flux and as a fission booster for dial a yield (once again, to increase neutron flux). Both of those are just as important for fission weapons as they are for fusion.
Importantly, alpha decay creates helium pockets which is a neutron moderator and screws up the bomb.