> - the default value is missing some values you would expect, like /use/local/bin and /usr/sbin for root.

What do you mean by "you would expect", that doesn't also apply to systemd timers? /opt/foo/bin is not in the path. Would you expect that?

And if this is an objective problem, can we just change the cron default PATH?

> - on some distributions (for example Arch Linux) the man page doesn't even say what the default path is, or recommend setting it.

Send a PR. This doesn't seem like an inherent problem.

> - if you need to add something to the path for a single script, you either need to wrap it with a call to env, set it in a wrapper script, or set the path before the entry and reset it afterwards

Or on the line, right?

    * * * * * FOO=bar $HOME/bin/foo.sh

The line can get long, but is this really a problem?

> - you can't use ~ or $HOME in the path, you have to write out the full absolute path. Which is particularly annoying for user crontabs.

This is incorrect. You can definitely use $HOME in user crontabs.

I'm still not seeing something that warrants a rewrite. (except what you did not mention, which is the ability to run "trigger this now" as a missing feature)