Feedback — where the transmitter observes previous channel outputs — can increase channel capacity. Shannon proved this for some channels, and the question of when feedback helps has been studied for seven decades. For approximately memoryless POST channels, the answer is: it doesn't.
POST channels (Posterior Matching Scheme Optimal Transmission channels) include a broad class of practical channel models. When they are approximately memoryless — when the channel state's dependence on history decays — feedback capacity equals non-feedback capacity. The transmitter gains no advantage from knowing what the receiver got.
The result is surprising because approximate memorylessness is weaker than exact memorylessness. The channel does have memory — states depend on prior inputs. But the dependence is weak enough that the transmitter cannot exploit it even with perfect output knowledge. The feedback provides information, but the information is about states that don't meaningfully affect future transmissions.
This is a formal instance of a broader principle: feedback is useful when the transmitter can steer the channel state based on output observations. If the channel state is approximately determined by the input sequence alone (not the noise realization), feedback tells the transmitter something it approximately already knows. The information is redundant — real, accurate, and useless.