Compare utxo to their own books? What are you talking about?

You don't own a utxo unless you hold keys. Just like you don't own a dollar unless you own coin or cash.

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Compare a custodian's utxo set to the custodian's liabilities.

I understand what you're saying, bitcoin is obviously much easier to audit, I just can't see any reason why sufficient numbers of people will ever care.

I agree.

I also fail to understand why I should care? If they want to invest their fiat into bitcoin, then never actually withdraw it, so?

Stupid? Yes.

Pointless? Yes.

My issue? No.