Even with my online groups, most people have still opted to roll live rather than go through the hassle of formatting online sheets.
Interesting. I also allow real rolls and lot of players use it, but mostly because its for fun. In my experience the online sheets are not a hassle at all, you click on your skill, it gets automatically rolled, modifier already applied, result immediately.
1. The majority of games I engage in from either end of the table are ones where positioning, distance and things like cover actually matter.
They matter in my games too. "I get to cover behind that column [you described]", "Can I shoot XY?" etc. they all matter, they just get communicated differently. Distances I'll admit matter but only the (in my eyes) interesting parts. I don't care about having 5 feet differences. I'll abstract distances as "melee, close (within normal movement), near (within dash), far (everything else)"
These are the difference group of distances that matter IMO. 5 feet squares are also an abstraction after all for ease of use, theoretically you could be 5 inches to far away to be in reach but I think we all can agree that this would be a bonkers level of specification.
I have very poor spatial imagination and memory, so keeping track of everything in the environment that's relevant is functionally impossible.
If you try to emulate grid combat in TotM I think nobody has the functional capability of keeping track of all the spatial relations. But usually I only memorize "Aragorn and Gimli are in melee with the orks, Legolas is sniping from the cover of the trees, Merry and Pippin are hiding in the ruins at the side of the battlefield" and again I use pure TotM rarely. Usually only for simple easy encounters with small number of enemies in simple battlefield. For everything else I use tokens for the spatial relations. Sometimes draw a quick small abstract map or draw zones of the battlefield on cards ("forest, open field, ruins") where the tokens can get placed.
In my experience as someone who used all methods, this leads to less players staring on the tabletop board of a map and more roleplaying in combat. Also I can always improvise a battle and the players never know it (if its improvised or planned). Plus I don't feel tempted to railroad players in a combat situation because I put 2 hours preperation in a detailed battlemap (I experienced this multiple times as player with other DMs). I also can do dynamic battlefield with moving terrain or objects quite easy. Try to have a fight on airship that breaks apart on a grid map.
That doesn't mean I never use detailed maps btw. I like to change my tools depending on situation and context. If I know the big boss finale will happen and it is supposed to be an epic, tactical, long fight, than I will pull out the detailed grid map. But when playing online I am basically forced to do grid maps only. All other approaches don't work as well online.
(Now we only have talked about battle maps. In online play usually players get a full dungeon map which completely transforms D&D in a board game. In personal play I let them draw a map and only describe their environment.)