You didn't seem to read what I wrote: it's only recently become "etiquette" to do this.
I'm simply pointing out that this is a fairly recent thing.
I typically remove my hat, but there have been times when I don't have the time (someone is a foot away as I take my ball out of the hole, etc.).
It's weird, because in the mid-90s people (at the very same country club - I was a junior member then so I paid close attention to what people did so I didn't offend anyone, as we juniors had to really watch things and not cause any problems):
- never wore jeans into even the grill room let alone the dining room
- always took off their hats inside, even in the grill room
- almost never took their hats off outside (same goes for sunglasses)
Nowadays, the same members (in many cases) or at least the same membership at the same club:
- wear jeans into the dining room sometimes (not jeans with holes or anything at least, but "nice jeans" are still jeans)
- sometimes take their hats off, but not typically
- ~60% take their hats off on the 18th (many of the 40% probably figure they're the same guys they play with every week so whatever).
Men used to doff their caps to women. That dates back a long time ago. Men with armor on used to raise the visor so they could see each other's faces when addressing people higher in rank than them, and that dates back a long time as well, but military men don't take their hats off when addressing superiors or underlings (they salute, of course). Hogan, Snead, Palmer, etc. didn't doff their caps to shake hands.
Augusta National is probably one of the most "traditional" places you'll find and except for making Rickie Fowler turn his hat AROUND, players wear their hats indoors there! They shake Billy Payne's hand on the first tee while wearing their hats, Nicklaus, Palmer, and Player. If anyone could enforce the rule of "no hats inside" or "doff when shaking hands" it'd be the folks at Augusta.
It strikes me as one of those funny things: WHY is it a sign of respect? Why would you go so far as to make a judgment on someone who DOESN'T remove his hat? You can still look him in the eyes. You're still shaking the guy's hand. What's it to you whether he's holding his hat in his other hand? Maybe he's got bad hat hair, or is embarrassed of his growing bald spot, or can't hold on to his ball, wedge, putter, and hat at the same time?
I take my hat off most of the time but not all the time (again, sometimes people are too close or the person I'm playing with is familiar enough with me that handshakes are more awkward than doing nothing).