Why do we not verify this type of issue when the funds are deposited and often only when the funds are withdrawn?

This is an approach developed on the basis of good practice. The vast majority of customers prefer to be able to dispose of their funds as soon as they make a deposit and leave the verification issues for when they make a withdrawal out of the exchange.

However, this is not the rule; often verification of the source of the funds is a condition for adding these funds to the user's balance and this happens after the payment operator or the currency network in question has received information about the deposit..