I want this too, but more for combat reasons than social. Sometimes with the battle music, the loud sound effects, I can miss the pinging sound of a party chat (not the s.e.) and sometimes the chat log scrolls fast so I might miss what the party is trying to say (that isn't some stupid announce macros that aren't needed). Yes, people use voip these days but non voip pugs exists and strategies differ group to group and sometimes mid combat chat to adjust strats can happen instead of just wiping and then discussing why a person didn't do something. So I think better visibility can help.

It doesn't have to be a full chat bubble, I'd be fine with just a (!) or a (...) chat bubble popping over someone's head or at the edge of the screen if the player is not in view and only pops up if it's a line typed up manually, not a macro. And again, it can be optional and be set to whatever chat type you want (party, fc, ls, say, etc).