Why? ... your opponent may be non-rational in one of a trillion of very realistic, very common ways ...

This is a fair point. For games people are not familiar with, have not played to death, this is absolutely true. For the games people have played a lot of, (or have had their genes and memes evolved under and contributing towards their moves), anything but what the Nash equilibria does must get outcompeted. Playing poker against a novice, there should be options much better than Nash. Against a pro? Not so much. Against a hustler (who isn't actually cheating)? Well, they're optimized to take advantage of novices, by leading them into bigger bets, so you can probably take advantage of this by not scaring them off by playing too well too soon.

maybe he'll cooperate because of his personal moral/religious views, maybe he'll defect because he doesn't want to think of himself as a 'sucker'.

These are, of course, part of the utility function -- and if you don't know that modeling is a bitch.

most of which have a terribly flawed rational process.

Most people do not play by reasoning it out to any great depth at a conscious level. They play by gut instinct, set by genes (and memes) and shapened by experience. For games where the genes are relevant, this is going to push towards Nash. Experience is also going to push towards Nash.