I'm not sure how that works, as I've never gone through a KYC procedure successfully in the past few years.  I've tried, but the pics I've submitted were never good enough, but that's another story.
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There was an article about AOPP by Bitcoinmagazine

Why implementing AOPP could pose a risk to bitcoin long term

In Switzerland, anyone that uses custodial exchanges have to get verified, if users are verified and want to send bitcoin to  external wallet address, AOPP helps in a way the user of the exchange that have been verified can be able to provide prove that he/she is the owner of an external wallet address.

I do not know the principle behind it, but I know there has even been a way this can be done which is signing a message with an address but which is not a good way either because it is a mean the government are invading privacy. There is nothing worse than wallet developers providing this in my opinion as the government are having means (provided by wallet developers) to invade privacy.

I just like that few wallets that were supporting AOPP before are no more supporting it. Without AOPP, there has always been data leak on exchanges, with AOPP, the severity of exchange data leak might be worse on bitcoin users as privacy is becoming impossible.