Not as pointless as most people intuitively think. What if the chat server you're using is compromised by a hacker trying to make a name for themselves and they publish all of the chat logs on bittorrent?

Some examples of comments in a private chat that might at first appear like they don't need encrypting, but might come back and bite you in the arse if they ever get published:

"God work is boring today. Need to update my CV/Resume"

"Bob was a bit of an idiot last night wasn't he"

"Thinking of skiving off work tomorrow."

"The wife has been nagging at me all afternoon. Fancy a pint later?"