Is it possible to have a proof of reserves for cashu mints?

[Nuhvi]

I am aware of mints reputation based on reviews on Nostr. However, I wonder if some evidence of rug pulls can be more effective and more socially scalable than a WoT, basically a proof that all issued tokens corresponds to a sum of an onchain UTXO possibly representing LN channels, then whenever a withdrawal from that UTXO has no corresponding authorization from a token owner, the reputation of the mint can be burned in an observable manner, possibly by publishing the contradiction on L1.

This doesn't prevent rug pulls, but it might prevent repeated rug pulls, and immensely favors long running mints without any incidents.

Why is that impossible or impractical or not desirable in the first place?