Yeah, Kirk did play fast and loose with the Prime Directive - but often with extenuating circumstances.
In at least one case, he was over-ridden by higher authority in the first place ('A Taste Of Armageddon').
In some instances, he was trying to undo or redress imbalances brought on by the interference of others ('The Omega Glory', 'A Piece Of The Action', 'A Private Little War' and probably others)
In some other instances, he was dealing with crazy computers that had enslaved the human populace, and frozen any kind of development by them ('The Apple', 'Return Of The Archons', 'Spock's Brain'). Maybe the PD had a specific clause for this kind of situation?
It is said, time and again, that starship captains have quite broad discretionery powers. They need them - dialling up Star Fleet Command and then waiting on a ruling from them on something is often just not practical. Add to that, there will be times when someone on the spot is needed with the authority and judgement to NOT merely hide behind the rulebook.
It seems likely that, everytime Kirk did some PD hijinks, SFC required a complete report from him and might have even had a formal enquiry on his actions - with the very real possibility that he would be relieved of command if found wanting. One can then infer that, for the most part, they found his actions at least acceptable.
Noting the differance with Next Gen, where the PD was taken EXTREMELY seriously. Too much so sometimes, IMO. There were a few times where the PD was invoked that made absolutely no sense at all, and times when it just seemed to be an excuse for passive-aggressive behaviour.