Why do some US universities ban first-year graduate student from working outside TA/RA?
It seems obvious that they want students to focus on their studies for the first year. 

I don't know why they feel this way, but as a state funded education that is putting public resources into a student's education, they don't want those resources "wasted" or used ineffectively. 

If a student proves him/herself the prohibition ends. I would hope that the last part is reinforcing this. TA fine. Research fine. Because we can have some control over how much effort is spent there. 

I would object to such policies if they excluded financially needy students. I don't know how they manage that issue. 

But even institutions that run graduate schools but are not publicly funded still subsidize student education to some extent. As high as tuition can be at some places it is often matched by other sources. I'm assuming the institutions are non-profit. Not all are, and that has its own problems, but those are very unlikely to have such rules.