I use tmux locally even though I run i3 as my window manager. Mostly because I configured tmux to show the current directory and git branch (if in a git directory) so I can keep my prompt a clean "$".
I guess you can hit enter before every command is entered to get the correct time but that is a lot of wasted space!
Maybe I'm getting too minimalist but I don't see the benefit to productivity in these over the top prompts.
If anyone is curious what it looks like: https://imgur.com/Xx19sFn.png