Because that would involve bringing along a reactive metal, bringing one H2 molecule with you is less mass than any of the metal atoms that would react with H2SO4 to give you the same amount of hydrogen. But perhaps more difficult to handle as a gas.

You could bring along MgH2, then once you hit the atmosphere, you can thermally decompose it into Mg and H2, then react the Mg with sulfuric acid to get MgSO4 and another H2.