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I would argue in a GW to them that reporting after payment is not really in their best future interests, and that deletion would be beneficial to both you and them.
In this day and age of consumer access to their credit reports, a primary reason why debt collectors report their collection is to put pressure on consumers to pay in the hope that they can reduce impact on their credit score.
If they conduct a practice of reporting after the consumer pays the debt, I would argue that it undermines future consumer incentive to pay.
They are capitalists, not humanitarians. They are more concerned with collecting $$ than promoting the integrity of the credit reporting system by supplementing consumer payment history for view by others.
Perhaps an appeal to their wallets.........?