I'm pretty sure they will get to Punta Cana sooner or later. Nobody thought it would catch on in the capital, and in truth there are reports of Uber drivers being chased off the airport. But Uber is a mighty organisation with far more money and power than a taxi syndicate here and I don't think they are used to failing. In Santo Domingo they have had their problems, put the prices down, then up, then down again, then up again, drivers walked out in droves, quite a lot of issues. But they've recently introduced the UberMotos and it feels like they are here to stay.
The thing is that everyone who works for Uber is independent. If a driver is threatened in Punta Cana, so what, maybe that driver leaves, but there will still be plenty of others to take his place. So I reckon it will get there soon.