I think Kirk hated the uniform. In almost every scene he is wearing it, he has it unclasped. Only when he is doing anything official does he have it buttoned up. In fact, in most of the movies, he wears an alternate uniform.
The last major change was to redesign the flap of the double-breasted jacket so that it would actually open. This was something Meyer wanted, because he felt the lighter color on the inside of the flap would frame the actors' faces better.
Other than the Dramatic/Cinematic reasons behind the scenes, in universe I'd say it's a bit like loosening your tie after work or whatnot.
Technically, it's probably supposed to be closed while on duty, but depending on your commanding officer, you might get away with leaving it open. It's a bit like Picard allowing Troi to wear whatever she wanted until Jellico came along and made her wear a regulation uniform. If your Captain doesn't mind, leave that sucker open.
Other than the already mentioned behind the scenes reasons, I'll also add that it gave the actors something to play with. Actors like to do things with their hands when they can. It also allows the dramatic opening, like the dramatic sunglasses removal.
Having worn one, I can say with confidence that one major reason to unclasp them is because they're not all that comfortable. The modern day equivalent is unbuttoning the top button of your shirt, or loosening your tie. When worn clasped, you're wearing a turtleneck sweater, and 4 layers of wool fabric over your chest, with 2 layers of piping, lined with bits of metal chain, and snaps. While the turtleneck keeps all that mess from rubbing on your throat, it can get quite warm, and a little bit irritating having that lump of fabric at the throat.
Popping the snaps on the flap drops half of that fabric away from your throat.
I'm sure the other reasons (framing faces/bloody hand prints) are perfectly valid.. but under studio lights, jumping around in that thing doing take after take.. I couldn't imagine. Wearing one at summer-time conventions was uncomfortable enough as is.
it always felt like cheating to wear my Third season TNG uniform. in comparison, one layer of Polyester was sooo much cooler.
Personally, I think that it makes the Uniform look a bit more dignified, don't know why, it just does. I also would like this kind of thing to be added to the Veterans Uniform, because it reminds me so much of the TWOK Uniform, that's the main reason I like it. But anyway, I've worn the Uniform, it is kinda uncomfortable, so I guess that's the reason/