It's important to handle many socket connections for once. Where "many" may be in the order of million. If you wonder who on earth need that many connections, there are many use-cases like pub/sub servers. Native threads and processes use an excessive amount of ram and context switching is way slower (more so for processes) in comparison. Not to mention asyncIO allows sharing memory (without copying), which processes will not (message passing through pipes or sockets is way slower) and since asyncIO is non-preemptive, it make it easier to deal with shared state than when using preemptive native-threads.

Doing asyncIO was a way to solved the c10k[0] issue back in the day.

[0] https://en.wikipedia.org/wiki/C10k_problem