Why the timestamps are that important? Honestly asking.
You can always time your commands with "time".
I personally use a modified zbell (in zsh) to give me a notification when a command finishes after 30 seconds, and send me an email if it takes over 2 minutes.
When you’re debugging, especially a complex system, especially during an outage or postmortem, understanding when your commands executed relative to when your log lines appeared is really helpful.