Daniel Trombly sums up my reaction to this Petraeus-for-VP article:

This argument for Petraeus as VP is pretty much entirely mystifying. Why on earth would Petraeus do it?

That’s a good question. As far as I can tell, Petraeus would have no incentive to accept the offer, not least because he would have no interest in political campaigning and the constant attention and scrutiny that come with being a national candidate. “Surge”-related Republican hero-worship aside, I’m not sure there is much reason for Romney to make the offer. A Petraeus selection would draw attention to how unprepared Romney is by comparison. It would suggest that Romney intends to contest the election on national security and foreign policy issues rather than on the economy. That would be a strange plan for the challenger at almost any time, and it makes absolutely no sense at present.

Paul Miller’s argument for selecting Petraeus resembles a lot of the 2011-12 speculation about fantasy presidential candidates. Miller laments the poor quality of the current group of prospective VP nominees, declares the entire Republican bench too inexperienced (Rubio) or unwilling (Daniels, Christie), and then promotes the only person able to survive this process of elimination. The argument for Petraeus as VP is also a complaint about the quality of the presidential nominee. Romney is inexperienced and unprepared on foreign policy and national security, and so are most of the possible VP nominees, so it becomes necessary to find someone to fill that gap.

It’s not that different from what we heard from earnest Rubio or Ryan boosters when there was still some hope among movement conservatives that one or both would ruin his future career with a pointless presidential campaign save the country. There is no consideration of the political liabilities or problems that might come with the selection. Petraeus’ favorability rating is so high precisely because he is perceived as a military professional who has served under administrations of both parties. If he became the nominee of a major party in an effort to defeat the sitting President, that reputation for non-political professionalism will fall apart quickly. Why would Petraeus risk wrecking his public image for the chance to be Romney’s Vice President?

There is also a questionable assumption that Petraeus will enable Romney to criticize Obama’s foreign policy record with more credibility:

Additionally, Petraeus would bring foreign policy expertise to the ticket, balancing Romney’s focus on economic issues. If Obama really intends to claim that his foreign policy accomplishments should earn voters’ respect, there is no one in the country with more credibility than Petraeus to take Obama’s argument apart.

That raises the question: does Petraeus have a great interest in taking Obama’s argument apart? Is he going to echo Romney that cooperation with Russia is detrimental to U.S. interests? Would that be a credible criticism just because Petraeus is the one making it? Since the U.S. has not been “betraying” allies and clients around the world for the last three years, it doesn’t make claims that it has more credible if they come from Petraeus. I could go on, but you get the idea. Romney’s foreign policy critique isn’t credible, and as his running mate Petraeus would be expected to endorse that critique. Instead of boosting Romney, the pairing would probably just drag Petraeus down.