It doesn't fundamentally solve anything. You want to be able to identify a specific person or at least a relatively expensive device so that if you ban them they stay banned.
This is the exact method used to secure iMessage against spam: secure attestation and ‘console’ bans of devices (reversible by iirc phoning support, indicating who you purchased the used device from, and providing an ID). But Google is trying to pull a Windows 11 “TPM or die” conversion on the public Internet via Recaptcha. Welcome to the attestation wars, unwitting websites :)
The people who this method is most hoping to stop are the least likely to be impacted by it in the long run.