If you give your money away and trust a 3rd Party.. then there is no reason in using Bitcoins.. u could just
use FIAT. I think centralizing a decentralized system makes 0 sense.
The only possible idea of investing in a Bitcoin bank would be a high interest rate..
But this, to be honestly, won't ever happen
For you there might not be any reason
But for other folks there could in fact be plenty of reason in using a Bitcoin bank. And still more so if Bitcoin banking services would be offered by regular banks. In that case you wouldn't need to pay hefty commissions on fiat withdrawals as well as deposits from and to Bitcoin exchanges, and I'm strongly inclined to think that the former will be more reliable overall than the latter (given all the hacks and scams that we've seen during the last 4 years)
I think you don't need a Bank to have low commissions on deposits/withdrawals.. a Currency exchange would be enough, no need of a real "Bank"
And even against those Hacks you could just use a Hardware Wallet.. But as you mentioned.. IMO a Bank is not needed.. may be different
for other persons