Two positive charges on a small molecule is too much for it. It's energetically unfavorable, so instead, there is always plenty of water so H2O + H2SO4 gives H3O+ and HSO4- then H2O + HSO4- can give H3O+ and SO4 2- but this is not as favorable (i.e. energetically profitable) as the first, so if there is plenty of water, mostly it is HSO4- but there will be some SO4 2- ions.
Charge, whether it is positive or negative, has to be spread out over the molecule to reduce the electric field energy. The bigger the molecule the easier it is to spread out the charge, (reduce the electric field strength). It is easier to generate SO4 2- than H4O 2+ because sulfate is much bigger than water.