It's going to be much more useful for the US if they don't overthrow Iraq because if there is a civil/proxy war within iraq then that has a much better chance of drawing out Iran to stabilize their border regions and it will allow ISIS to do exactly what it has done time and time again by weakening and destabilizing neighboring countries.

If it was about overthrowing Iraq they'd do it directly, just like last time.

They want a casus belli and if Iran is acting outside of its borders to strike at ISIS then the US can point to that as an excuse to deploy troops right on the Iranian border to stop their "expansionism" and "foreign interference." Then all they need is an attack on US soldiers or diplomatic staff, or at the least an event where a handful or more of Iraqi citizens are killed in an Iranian strike against ISIS operating in Iran, and they have their next Benghazi rallying cry to drum up support for "defensive" attacks on Iran.

They just dropped thousands of trained, blooded ISIS fighters into Iraq. The most important part of those numbers isn't the people who can pick up guns but the ones who can recruit and organize and especially the ones who are experienced commanders. We're talking about 1,500 cut loose in Syria (right on Iraq's border) and 7,500 being transferred to Iraq. That's a whole lot more than a dozen.

The following is from a strategic analysis document titled Which Path to Persia? Options for a New American Strategy Toward Iran, starting on page 64 (my emphasis):

In theory, the United States could mount an invasion [of Iran] at any time. The president could order an invasion tomorrow, which would seem to make this option very time efficient. But the reality, of course, is that it is highly unlikely that he would do so, and there are many hurdles to be cleared before the first troops would hit the beaches. Although an invasion might accomplish its objectives more quickly than Engagement or the various regime change options, it still would require months of military and logistical preparations, and might take even longer to lay the political and international foundations.

It seems highly unlikely that the United States would mount an invasion without any provocation or other buildup. Even in the case of the Bush Administration’s march to war with Iraq in 2003—which was about as fast as it is possible to imagine—there was almost a year of preparations, starting with ominous statements from the administration, new UN Security Council resolutions, a congressional vote, the buildup of forces, and an ultimatum to Saddam Husayn. Moreover, in the case of Iraq, there was a legal basis that the Bush Administration could rely upon (the same basis that Bush 41 and Clinton had used to justify various air and missile strikes against Iraq during the 1990s).

In the case of an invasion of Iran, there does not yet seem to be a legal predicate to justify the use of force—which is important more because it is required under domestic U.S. law than because of the need for international legal sanction. If a provocation or a UN Security Council resolution is needed to provide that legal basis, that also will take time. In fact, if the United States were to decide that to garner greater international support, galvanize U.S. domestic support, and/or provide a legal justification for an invasion, it would be best to wait for an Iranian provocation, then the time frame for an invasion might stretch out indefinitely. With only one real exception, since the 1978 revolution, the Islamic Republic has never willingly provoked an American military response, although it certainly has taken actions that could have done so if Washington had been looking for a fight. Thus it is not impossible that Tehran might take some action that would justify an American invasion. And it is certainly the case that if Washington sought such a provocation, it could take actions that might make it more likely that Tehran would do so (although being too obvious about this could nullify the provocation). However, since it would be up to Iran to make the provocative move, which Iran has been wary of doing most times in the past, the United States would never know for sure when it would get the requisite Iranian provocation.

In fact, it might never come at all.As far as the time requirements for the military side of the option, it might take a few months to move the forces into the region, and then anywhere from one to six months to conduct the invasion, depending on a variety of circumstances—particularly how much U.S. forces had been built up in the region before the attack was launched. Nevertheless, it is important to keep in mind that the rapid launch of the war against Iraq was a function of the inadequate number of troops and planning for postwar reconstruction. Since Washington would not want to repeat that tragic mistake in Iran, the buildup for an invasion of Iran would have to be bigger and thus take longer to complete than the buildup for the Iraq invasion. Finally, the preparations for Iraq were greatly aided by a superb network of American bases in the Persian Gulf. Absent some dramatic Iranian provocation, it seems very unlikely that those same countries (Kuwait, Bahrain, Qatar, and Britain, in particular) would allow the United States to use those same facilities for an invasion of Iran, potentially further lengthening the time required for the invasion itself.