An instant messaging client shouldn’t be executing arbitrary remote code, no.

It's not really possible to prevent that. E.g. a well crafted image can easily trigger an RCE on some older versions of Android: https://nakedsecurity.sophos.com/2019/02/08/android-vulnerab...

Issues like this exist at all layers of the stack, so anything touching the internet needs regular security patches.

I agree completely. But, I also think that in most cases, if a simplistic piece of software like an IM app needs a security patch every three months, regularly, it's a sign the attack surface is too large.