In legalistic terms, the Fed isn’t (currently) allowed, let alone required, to take over. It has no legal authority to do so. Congress, of course, can theoretically give it that authority, but what would be the effects of the Fed overtly nationalizing all banking? The “middlemen” banks’ shareholders would either find themselves holding worthless assets, or (much more likely) the Fed would pay them off. However, this compensation would still lead to an economic loss, in the sense that exchanging their shares for dollars wasn’t the most utilitous action to take in the eyes of the shareholders - for, if it were, they would’ve done so on their own.
More importantly than this, however - because the Fed was essentially created by and for the “middlemen” banks, it seems very unlikely to me that the latter would just roll over and let their operations be taken over. Again, the point of the Fed has always been to better ensure profits for the “middlemen” banks in their fractional-reserve banking operations. I present the recent bank bailouts as evidence that it’s the (big, wealthy) “middlemen” banks who are really running the show.