With a cooperative scheduler, you will, sooner or later, experience some form of starvation. The most obvious is the process that just infinitely loops, but less obvious situations will end up popping up too; calls that you thought were handled by the event loop but turn out to be blocking and add up when you start calling them at scale, strange behavior when you have a set of processes that turn out to yield far less often than you thought and the system starts behaving with much higher latency than it should if you get too many of them, and all kinds of such manifestations. There's also the inability to create things that watch other things; if something does go spinning off into infinity, nothing else gets to run to kill it.

You can hack around many of them, but you eventually hit a wall, and the effort of the hack increases rapidly.

Note I didn't really use gevent in this reply, this is just about cooperative scheduling. There's a reason why we've all but completely abandoned it at the OS level for things we'd call "computers" (as opposed to "embedded systems" or "microcontrollers", etc). I tend to consider cooperative scheduling an enormous red flag in any system that uses it... and yes, that completely and fully includes the currently-popular runtimes that use it.