They are here to stay... Just like the snakeheads, nature will adapt and be fine.
I dunno about that one. There are some papers that there are noticeable declining in native populations when Asian carps take over the river systems. Buffaloes, gizzard shads and paddlefish showing the signs of starvation by being in poor conditons and the native population declines. Even the asian carps are being starved in some sections of the river where overpopulation occurs. It's hard to say that nature will adapt and be fine...
You are right, they are here to stay but that doesn't mean nature will adapt and just hopefully be fine.