My understanding is that if a uploader does that, youtube has to decide whether to keep it up. If they do, they can then be sued by the right holder if it does infringe. If they take it down, no one can sue them.

So that's a huge incentive to just take everything down.

Effectively the whole point of DCMA (this part at least) is to pierce the common carrier protection platforms have.

Am I wrong? If so, any idea what Youtube don't just let people counterclaim and leave everyone else to argue it out in court?

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.