I've always had the suspicion that anyone who would actually be an excellent president would have too much integrity to do that which it takes to get elected as president.
I have a sneaking suspicion that integrity is not a functional or desirable trait in a politician. What we really want in our political leaders is someone who will be sneaky, underhanded, ruthless and downright duplicitous; on our behalf. Integrity is nice to have and desirable in your neighbors and friends, but politics is about survival, ethics is secondary (or rather personal and societal survival _is_ the greater good).
Maybe it should be a Hitchhiker's Guide to the Galaxy type situation.