They certainly will thrive, and already do to a larger extent, but it's all short term with how even Binance will eventually find itself in a position it can't escape from anymore. I'm not using Binance personally, but there will be a day where Bitmex (my current platform of choice) will also force its users to walk themselves through some sort of verification process.

The rest of the services retaining their zero verification advantage will contantly have to worry about the authorities raiding the crap out of them. You can try to keep hiding behind proxies as much as you want, but eventually the hammer will hit you so hard that it means game over. I personally don't care about these services specifically, but they always affect users which is the sad part, because the government won't give you anything back once they seized the assets of an illegal operation.