Here is why I think that Kirk is the biggest violator of time. He was captain during a time frame when interaction with time travel was NOT something to be avoided but was sought out. Back in the TOS/Movie time frame, time travel is something new and it is being explored and played with, as Christopher showed in his Forgetten History novel.
But as time wore on, it became apparant how dangerous time travel was and how one small misstep could have huge ramifications. Look at the recent Myriad novel that shows how history was changed when Spock was killed as a child and someone else was in his role as XO of the Enteprrise. How different the galaxy was shaped by one man's absence.
The fact that there is an entire department of the government (with counterparts in other society governments), classes taught at the academy and its own Prime Directive shows that Time Travel is not uncommon. However, filmed Canon has shown that it is VERY rarely caused by the crew themselves and is more often than not caused by some outside influence which most likely cannot be duplicated.