An invasion likely would turn into a quagmire, but what keeps regime proponents eternally hopeful is that unlike Afghanistan, Iraq, Vietnam, etc, Iran has a robust political system. The dictatorship notwithstanding, it has a vibrant parliament and, by global standards, a decent electoral system. The Ayatollah rules by following the maxim, keep your friends close and your enemies closer. If you could excise the Revolutionary Guard (a big if), you wouldn't necessarily need to change the government or its institutions. The existing liberal and moderate factions could quickly fill the vacuum, and would be happy to do so. You wouldn't get a pliant Iran, but that's for the better.

So by invasion the idea would be to rapidly, physically excise the apparatus the Ayatollahs use to maintain control. The structure and identity of that group is well known. It's a large group, and you couldn't catch all the leaders, but so long as you can stop their ability to enforce their rule through execution, you give the rest of the country time to shut them out of the institutions. In theory just weeks.

The problem is the very thing that makes regime change a plausibly good idea--a stable polity and modern, liberal-ish institutions--is the very thing that could result in failure. The Ayatollahs understood that a fragile, backwards system would be a weakness to their rule. Their military and bureaucracy are professional; they know how to follow orders, without being micromanaged, and even if everyone wants regime change, there's a huge collective action problem.