I'm going to make a few assumptions here

1) You're not talking about refunds. Most payment processors, like bitpay, offer some form of refunds.
2) You're not talking about sending someone BTC because you could do that as long as you know their public wallet address. Clearly you can do this from within coinbase.

What it seems you want is to initiate a transaction in BTC and have it delivered to someone is USD. Correct?

The problem is that is not a payment processor but a money transmitter, ala Western Union. Payment processors avoid doing this because they have to register as MSBs, at least in the US. I believe Coinbase has their MSB license and you can certainly send BTC to a user's Coinbase account and they can cash it out in USD.