We consider bottlenecks of TCP throughput in scenarios with edge clouds and 5G cellular networks. By numerical examples from measurements in real networks, we show that edge clouds indeed improve throughput but that several, nonnegligible bottlenecks remain. We therefore devise a concept where edge clouds connected directly to the radio access networkcan increase their transmission rates by relying on built in retransmissions (through quality of service features) and on the built in user fairness (through per-user buffers and scheduler policies). We then return to the numerical examples and show that our solution provides substantial gains and we concludeby identifying and discussing the remaining bottlenecks and the potential of an improved protocol.