Why do some US states have multiple universities?
Your question seems to assume the default is for all campuses to be the same, but there's no reason for this to be true.  For example, the UC schools are far more research-oriented than the Cal State schools.  There's nothing wrong with that: California wants to have some public research universities, but that doesn't mean every public university should be a research university.  That would be extremely expensive, and the net result would be either more research than the state wanted to fund or fewer universities.

There are many ways universities can vary (degree of research focus, graduate and professional programs, selectivity and prestige, etc.), and by default they will be different.  This is typical in U.S. states, not just limited to California.


  It'd be easier for the students, as they now wouldn't have to go through a transfer application process just to go to a different state-run campus.


That's not generally true, and indeed you can't easily transfer between UC campuses.  From this perspective, California doesn't have two public universities, but rather dozens of them.  It would require massive changes to make easy transfers work in practice, because some locations are far more popular than others and would be terribly overcrowded if everyone could transfer wherever they liked.