I can't say that would be impossible and not work. But if you look at what's out there on the market, that's not how the sustainable processors do it. Once you reach a few million USD a month, and chargebacks start trickling in, it won't take long for Stripe to connect the dots. The same players charging back against two or three of those accounts would be disastrous. Then Stripe or possibly the card schemes themselves will start looking into your businesses and cross reference cards and card holder against accounts with similar risk factors.
The good US-facing (and similar restricted territories) gambling processing is happening with the gateway, processor, and acquirer all fully aware of what's going on. But even there, accounts blow up from time to time and money is lost.