So far, private coins have not been excluded from exchanges, for example Binance still trades most such coins. Or smaller exchanges continue to trade too. But some private coins have their own DEX. I think that if delisting will start, many users will start to use such DEX rather than third-party services.
I've never spoke about third-party services. I don't even know what is that.. And you're wrong about delisting. Check out this article:
https://cointelegraph.com/news/binance-to-delist-privacy-tokens-in-france-italy-spain-and-poland