Alan Moore clearly thought Batman was at least somewhat insane, look at "killing joke."
I think it's a valid character interpretation.
I mean, here's a billionaire who lets the death of his parents at a young age define his life, refuses real attachments in favor of his stupid "mission."
He wants to change Gotham, so does he do it through running for office or trying to create political change in other ways?
Well, first off, the comics and films have both made it pretty clear that Bruce actively uses Wayne Enterprises and the Wayne Foundation to try to effect social change in Gotham. Bruce Wayne is a huge philanthropist, and the Wayne Foundation is very much the Gates Foundation of its world.
Secondly -- part of the point of the world of Gotham City is that it is an exaggerated version of everything that's wrong with modern urban America. We already see how often in real life electoral politics gets corrupted by money and power; there's a very real question about how effective running for office actually is in creating meaningful change. And especially in a heightened environmental that exaggerates what's already wrong in reality, I'd sure as hell be skeptical of the idea that running for office would necessarily be effective in Gotham City.
And while developing the economy and creating grassroots social change is certainly important if Bruce wants to save Gotham, so is being out there on the streets and saving innocent lives from immediate danger. And, remember, the other point of Gotham is that its police force is often either ineffective or corrupt. Under a normal social contract, the executive powers are delegated to an executive branch of the government (be that a President and his Army, a Governor and his Militia, or a Mayor and his Police); Gotham is a political environment without a functional social contract. Batman represents the citizenry reclaiming the executive functions normally delegated to the government as a result of governmental nonfunctionality.
(I love Batman, just pointing out the concept's a bit silly, and that anyone who behaved like him in real life would be deemed to at least have serious mental problems.)
Well, obviously it's a non-realistic environment and a non-realistic scenario. It's a world of heightened melodrama; it makes sense in the context of the exaggerated worlds in which the various Batman
versions play out.