If it's paying dividends, then it has de facto owners. Also, are there explicit constraints on "limited" balances -- eg fraction of money supply or fraction of GDP?
> If it's paying dividends, then it has de facto owners
No, it means the FRBs have legal shareholders. (The Fed per se doesn't pay dividends.) The Treasury pays interest, that doesn't mean it's owned by bondholders.
We could easily re-write statute so the Fed doesn't pay dividends (it would become interest on reserves), they're an anachronism from the days when the Fed had to compete to induce membership. But that wouldn't do anything practical and it also wouldn't satisfy the conspiracy theorists, so it's not really in anyone's interest to bother with.
> are there explicit constraints on "limited" balances
No, though it's maintained at an amount equal to banks' paid-in capital [1]. Broadly speaking, it's another anachronism.