While Batman clearly doesn’t possess any prior experience as an elected office holder, that likely wouldn’t prove to be too much of a roadblock, as Trump’s victory proves that past governing experience is not necessarily seen by voters as a prerequisite for the presidency. Bruce Wayne also has the money and resources to fund a robust (re)election campaign, should the need arise, without becoming beholden to big-money donors. There’s a chance he might end up impeached though, as Batman has repeatedly shown a willingness to bend or even break the rules if it means doing what he sees as the right thing. That kind of thing often doesn’t go over well with either the legislative or judicial branches of government.
Is considering the implications of a Batman presidency a silly thing to do? Yeah, kinda, although probably not as silly as actually voting for a fictional character. But after all the turmoil 2016 has put the world through, a little Dark Knight-based silliness is to be expected.