I tend to run too many people over that's my problem. Just drive all over the pavement and take short cuts through parks and on the beach etc. After a while you won't mind running everybody down as they are just a nuisance and in the way.
See your point with playing characters you might not really like that much - I've had moral conflicts in games before - like in Skyrim when want you to kill Parthanax but if something is necessary I'll do it regardless. With GTA it's a bit different in you're encouraged to let your hair down and go on the rampage - they're just sprites afterall.
Having said the above there's definitely a limit and overall I consider myself to play stupidly morally in the main as I can't get myself to play evilly. In Dishonoured I finished the game as good - there were two other endings - middle of the road and evil, dependent on how much carnage you caused throughout the game but it's a game and I meant to go back and see how much damage I could manage to get the evil ending. I bet Timey got the evil one if he even finished it.
Well. Probably an interesting subject for social scientists in the emerging field of cyberpsychology, how you play in morally conflicted circumstances and how easy it is for some to take the moral handbrake off.