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OpenBSD's crontab provides a `-s command` flag which does similar thing in principle:

"-s command

Only a single instance of command will be run concurrently. Additional instances of command will not be scheduled until the earlier one completes."

But I don't think it saves the state somewhere permanently, which isn't a big problem until cron's process dies for some reason.

If you need to save state across executions, you should write a daemon instead.

Then "rm" should be a daemon too

cron applies this very method of attempting to handle state by merely being a daemon, and it's not enough because cron can crash.

The approach you're suggesting is what led to the problem you're proposing it as a solution for.