Cooperation in a large wireless network (such as a cellular system) is shown to have certain fundamental limitations: namely, even perfect cooperation cannot in general change an interference-limited network to a noise-limited one. In contrast to existing literature that routinely assumes that the spectral efficiency scales with log P as the transmit power P grows large, we show the existence of a spectral efficiency upper bound that does not grow with P. The result uses well-accepted principles of information theory to reach the conclusion that it is not possible (or even helpful) to fully coordinate a large wireless network. Rather than simply low- and high-power regimes, there are three distinct network operating regimes: low-power; a DoF regime, where the log P scaling holds; and a saturation regime where the spectral efficiency hits a ceiling that is independent of P. Using a cellular system example, it is demonstrated that the transition to the saturation regime is operationally relevant and perhaps explains the lackluster gains from cooperation observed in practice.