Depending on the payment mechanism the act of issuing a chargeback causes reputation loss. With enough cases you’ll get your account closed. I’ve seen this happen to people doing a few returns on Amazon, or issuing a few chargebacks on their credit card. All were totally valid, but the customer was deemed to be not worth it anymore.
They paid, so it’s reasonable to assume they prefer paying and having that checkmark over not paying and not having that checkmark.
I don’t think canceling the payment will get them there or in the (again, reasonable to assume) even better for them “not paying and getting the checkmark” state.