Cooperation in a large wireless network with pilotassisted coherent communication is shown to have certain fundamental limitations, namely that even perfect cooperation cannot in general change an interference-limited network to a noise-limited one. Specifically, we demonstrate the existence of a spectral efficiency upper bound that does not grow with the transmit power, when channels are estimated via pilot signals. This is because pilot-assisted channel estimation is only possible within finite cooperation clusters, resulting in out-of-cluster interference that scales with the transmit power. Making the clusters excessively large can actually worsen this effect, nor does sidestepping the pilot-assisted channel estimation via noncoherent demodulation provide an escape. Using a cellular system as an example, it is demonstrated that the spectral efficiency saturates at power levels of operational relevance, indicating that the lackluster gains from cooperation observed in practice may be based on fundamental information-theoretic limitations, rather than current technology imperfections.