Actually, after thinking a bit more, I think my posts so far have missed the real question at hand: what is the root problem this rule is intended to address? Answering that will help us get to an optimal rule.
What I’m trying to say is: timeouts themselves are not actually the problem. They are no worse than resigning with one minute remaining, and no one would suggest disqualification for letting the time run low like that. The root problem is inactive players abandoning the tournament without clicking the “leave the tournament” button; timeouts, long-running tournaments, and dull later rounds without active players are the symptoms.
Unfortunately there’s no way to measure that directly. So we have to use a proxy – like timeouts, which does a decent-ish job. But, like all proxies, it’s imperfect, and rigidly designing a ruleset for the proxy instead of the root issue will inevitably result in occasional false positives.
That’s why I think there should be alternatives like a first strike (with a warning) or a button to rejoin (possibly with constraints, or requiring director approval).