Do We Care About Deniability in End-to-End Encrypted Messaging Protocols?

This is funny because I've heard a lot of discussion lately about do we care about deniability in our end-to-end encrypted messaging protocols? Do we care about the cryptographic ability to say, you can't prove that I sent that message under my public private key pair? And this seems to be like not the same setting where we care about, people talk about deniability. But it's a very related setting of people being like, ha-ha, like you just did that thing. So maybe if the like signing and sending of messages in this end- ToT protocol had deniability, this attack would be less devastating or something? What do you think?