On the other hand, all the financing needs will be covered by other means. These “non-banks” will have to obtain capital as equity and debt, maybe even loans from other non-banks, but certainly not as deposits.
What was the problem that we where trying to fix anyway?
Risk of financial collapse. Banks are risky because they have a lot of leverage, people more directly loaning money may take a 20% hit after a housing collapse, but that's not such a big deal.
And one of the reasons for the crisis was “shadow banking”, because many home loans were not really given by banks (some were directly created by other institutions, some were first created by banks but then packaged and sold). The subprime crisis would not have happened, at least to the same extent, if loans had been kept in the balance sheets of banks.
Including the United States' largest savings and loan association, until its collapse in 2008: https://en.wikipedia.org/wiki/List_of_bank_failures_in_the_U...
I suspect, but can't prove companies that need to demonstrate comptitence in lending to gain access to capital would be better at making loans than companies who gain capital by doing other things and then suddenly have access to a lot of capital and need to find a use for it.
Consider tech companies like Apple/Google/Microsoft have access to vast amounts of Capital yet does not really effectively use it for much.
Often the capital for many bank issued credit cards does not come from depositors at all.