A data breach on an IM app would be one of the most devastating leaks ever. And there’s just not that many legitimate use cases for keeping all history. If someone tells you something important you can make the effort to move it to their contact or notes in your phone.
Now, if the threat scenario is someone implanting a compromised version of the IM app on every device out there, and siphoning data from the device itself, then it's a completely different scenario.
[1] although this could be intercepted by an attacker compromising the IM servers, if the app is not distributed/P2P
You or the other person could lose the device and someone could use your PIN/password (something as simple as shoulder surfing while you use it). There could also be a leak in whatever cloud service you're using, or the data could get subpoenaed because of some dumb law that gets passed, some rogue employee, etc. It's a huge liability no matter how you look at it.
But for normal people, the biggest risk is companies using their chats to train models / dispatch ads etc to which the only solution is E2EE.
I also use the Note to Self which is built into Signal and appears just like any other conversation. I use that for temporary stuff like addresses and keep it clean.