i keep my glove on as i have built up my touch wearing it. i took it off a couple of times a few rounds back and just could get the pace of a put right.
tried playing this evening without a glove. after a couple of holes I didn't really miss it except that when gripping down on the shaft it felt too skinny so I'm getting mid-size grips fitted on the wedges.
Glove usually stays on , i find i forget to put it back on and end up rushing to do it before i take my tee shot at the next hole .It's okay for the pros it,s all they have to do between holes. No bag to carry ,trolley to pull etc.
I think they use the replacing of the glove to avoid eye contact with spectators , keeping the head down allowing the mind thoughts to be focused on the next hole, also keeps their eyes away from the scoreboard which a lot of them don't like to see
I've never even thought about having my glove on for putting (unless I'm out on my own and hit the ball stone dead for a tap-in).
Once I'm within full shot distance, it comes off into my back pocket. Never done any different.
As I've alluded to on here before I actually use my glove as part of my pre-shot routine whereby putting the golve on for a shot is my trigger to get ready to make the swing. I'll have already assessed yardage, wind, lie etc and made my club selection.
The golve goes on and it is the mental signal for my brain to focus on the swing element. One practice swing (at the moment focussing on making a full turn with the shoulders) then it is over the ball and execute.
Once I've seen the ball finish the glove comes off which tells my brain that it is ok to relax and switch off from golf mode until the next shot.
I think you get a better feel for the ball and feedback on the stroke without it especially on faster running summer (yeah today is Summer - NOT) greens