Both Fannie and Freddie buy mortgages, but your description is much more stringent than in truth. Fannie buys from big banks, Freddie buys from thrift banks; both buy conforming loans(conforming to their standards) which is a large part of the home buying audience. In addition to that, the non-conforming loans that you listed e.g. FHA and VA. Those government-backed loans are for special populations. These mortgages are assembled into MBS and then sold to investors; the banks that originated the loans get their liquidity back.