You can detect if a coordinator is attempting a Sybil attack. I explained this to you already, remember?

If your private coins were refused, it would mean absolutely nothing. You couldn't know if it's a Sybil attack or chain analysis refusing to accept private coins, and zkSNACKs wouldn't tell you why they got refused.
What you "explained" in that discussion, is that you already need to have private coins for the process to be trustless, which besides ridiculous, is also false, as the client software makes absolutely no Sybil warnings to the user in case their private coins are refused.