Yes, there are a lot of chances for governments to prohibit stablecoins for any reason. If anything like that happens then we cannot expect those reputed exchanges will keep listing stablecoins as they need to comply with government rules, they will simply delist stablecoins.
I'm not expecting people will go for P2P way of trading for centralized things. Because, if governments prohibit stablecoins then its value may not remain stable which means there will be no more point of trading them even in P2P manner. I am also in favor of decentralized stabelcoins. Hopefully we will get something like that in coming years.
They do not even need a reason,,, when have they ever needed a reason other than to remind the people that they rule that they are the ones in power?
Once governments control coins and learn how to use the technology for their own games, then they will allow it like China has allowed and developed their own China coin.