Why must the Federal Government operate a Social Security system? It's not at all clear what you're claiming there.
To provide uniformity across the playing field via federal law. But actually, that does not mean the funds need to be received into the federal coffers. My first reaction was to prevent the possibility of federal bailouts like I believe will be inevitable for these blue states.
One problem I can see with state run SS or the like would be the possible different state variations that would impact interstate job movement and the eligibility requirements from state to state. How would that work? Would states have different vesting formulae? How about the criteria for withdrawing? Where federal law does not regulate, the states can. So what the fed laws would be for all states is the real question. And now, what was within reach of federal politicians would now be within reach of the state politicians. I don’t put much faith in the latter either. I just don’t see the states doing the job any better (which is poor), while further complicating the whole system.