The idea is attractive (especially for draining), but once you try to map arbitrary inbound client connections onto backend-initiated "reverse" pipes, you end up needing standardized semantics for multiplexing, backpressure, failure recovery, identity propagation, and streaming! So, you're no longer just standardizing "reverse HTTP", you’re standardizing a full proxy transport + control plane. In practice, the ecosystem standardized draining/health via readiness + LB control-plane APIs and (for HTTP/2/3) graceful shutdown signals, which solves the draining problem without flipping the fundamental accept/connect roles.