Most of the people who make the argument I described probably believe the UN is the only legitimate body that could make this decision, based on some combination of practicality, historical precedent, and international agreement. And the UN absolutely has a mechanism for doing it (the security council). But one alternatively might argue the UN is broken/dysfunctional/corrupt enough that it can't be relied on despite having the "proper paperwork", just as national democracies can be for national affairs.

Unfortunately the non-democratic nations outnumber the democratic nations at the UN: https://en.wikipedia.org/wiki/The_Economist_Democracy_Index

It's why the UN has an obsession with a tiny democracy in the middle east and ignores the multitude of brutal dictatorships which oppress and kill far more people around it and across the globe.

Who decides when a leader is illegitimate or not?

Well, as always, who decides the leader is illegitimate? Are the Saudis illegitimate, according the the rubric we put on Maduro?

The UN deliberately has no mechanism for this because it's a talking shop intended to help avoid war by providing a talking venue. That's the whole idea, they're not the world police, there is no such thing. They're a forum.

I'm absolutely not defending any given dictator but history shows that every attempt to remove a dictator "for the greater good" is usually 1) selfishly motivated and 2) backfires horribly.

Right but "Don't kidnap/assassinate the enemy leaders" is often a good policy even when nobody will enforce that rule on you by force.

For example if your country is subject to a terror bombing campaign, it's very tempting to assassinate the one leader who had the power/respect/authority to order the attacks to start but often they're also the only leader who can order the attacks to stop

In the 1970s/1980s presumably the UK could have had IRA leaders Gerry Adams and Martin McGuinness assassinated. But it sure turned out to be useful, in the late 1990s peace process, that the IRA had identifiable, living leaders who could engage in negotiation, sign an agreement, and get the bomb makers to stop making bombs.

Russia is a regional power, though.

Public opinion?

The UN security council is one reasonable and popular choice, although it has lots of problems.

But enforcement is not even my point. I'm referring to a moral principle.