You could probably (I haven’t tested it) append the run time as a comment to the history using something like PROMPT_COMMAND and `history -r <(…)`, instead of cluttering the prompt with it. And the start time is already in the history, using HISTTIMEFORMAT.
This is why I really appreciate tools like Atuin. It augments your history with extra data such as the working directory, exit code, time to run command.
Per the Bash `history` manpage:
So this isn't true by default on many machines unless it is explicitly turned on. Once you do have it on, of course, then I agree.