Under the DMCA (technically Section 512), they have to reinstate access to the content at least 10 days and at most 14 days after receiving the counter-notice, in order to keep the safe-harbor (they have to wait 10 days to give time for the rights holder to decide if they want to sue the uploader).

> any idea what Youtube don't just let people counterclaim and leave everyone else to argue it out in court?

Essentially YouTube in the pre-Google days was purposefully uploading infringing videos, and Viacom (and others) used that to sue them and under the settlement agreement forced YouTube to build the Content-ID system and have a more lax takedown system.