He'd be a great VP pick though.
I thought in 2012 he'd have been the best VP pick for Romney, and I think I was definitely right.
Reality check: The GOP base will never accept a pro-choicer anywhere near the presidential ticket.
How much opposition have you seen from national Republicans to the candidacy of Scott Brown, who not only is pro-choice but favors an assault weapons ban? (Hint: none).
Republican voters are nothing if not tribal. See Pat Robertson's ill-timed endorsement of Rudy Giuliani in 2007. Also see how all the Republicans were hailing Romney as the second coming of Ronald Reagan during the fall of 2012, after his difficult primary performance due to his alleged squishiness.
The reaction amongst the GOP base to Romney's picking a pro-choice VP nominee would be "We told you there's no 'War on Women'!" (Another reason why he'd be an effective choice that year).