The banks that collapsed during the last crisis are not the kind of banks that take deposits and give out loans. They were the kind of non-banking businesses that you talk about.
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.