I agree completely. The disconnect you talk about has been prevalent in almost every modern era GTA protagonist, the only total exception being III's speechless Claude Speed. With Claude you rarely had any clues as to what was going on inside his head, he could be as crazy as the player wanted him to.
Tommy Vercetti and Johnny Klebitz both had tempers that one could believably see getting out of hand. Even so, performing other large scale crimes for the sake of it (like sniping civilians from rooftops, blowing up gas stations, etc) still made little to no sense if you were inclined to play in-character. Guys like CJ, Luis and Niko might have kicked ass at times, but they always came across as the type of people who were violent because they had to be. Not careful as such, but not going to go out of their way to cause trouble if it didn't need to be caused either.
Fortunately, hopefully, it looks like Trevor will break this mold completely. We don't know enough about his character quite yet, but Rockstar have said he revels in destruction. Between Trevor's madness in video clips, 'rage power' and drug use, I get the impression he's the character to embody all that good-time chaos the series is known for. At this stage I could see Trevor waking up, wandering outside and opening fire because it's not raining, or whatever bonkers reason his nutso-mind happens to think of in the moment.
