But here's some perhaps interesting information on top 5 shareholders of largest US banks [1]:
JP Morgan Chase: Blackrock 6.4 Vanguard 4.7 State Street 4.5 Blackrock 2.7 Blackrock 2.5
Bank of America: Berkshire 6.9 Blackrock 5.3 Vanguard 4.5 state street 4.3 Fidelity 2.1
Citigroup: Blackrock 6.1 Vanguard 4.5 State Street 4.2 Fidelity 3.6 Capital world Inv 2.4
Wells Fargo: Berkshire 8.8 Blackrock 5.4 Vanguard 4.5 State street 4.0 Fidelity 3.5
US Bank: Blackrock 7.4 Vanguard 4.5 Fidelity 4.4 State Street 4.4 Berkshire 4.3
So although yes this does go off the rails a bit, not unreasonable to question the (possibly perverse) incentives banks face given their ownership. Book by Eric Posner and Glen Weyl called Radical Markets explores those incentives a bit.
[1] Jose Azar et. al. Ultimate ownership and Bank competition https://papers.ssrn.com/sol3/papers/cfm?abstract_id=2710252