Steve going back into his existing past is physically allowable
if he was part of the history all along and we just didn't know it; both classical and quantum physics allow self-consistent time loops. The important thing, physically speaking, is self-consistency, so an event causing itself is allowed whereas an event preventing itself (and creating an irresolvable paradox) is not. A self-consistent loop where the time traveler was part of the past all along is just as physically acceptable as a branching-timeline model, since both of them preserve the existing history.
The problem is that Steve being part of the MCU's past all along is
narratively questionable -- it's hard to reconcile with the established history of the MCU or Peggy Carter, and it's
out of character for Captain America.