I got my current group together to run some 4E D&D when it first came out. At the beginning it was a lot of fun using the minis and maps. Combats were tactical, strategic and another problem to be solved by the players. With the flow of combat being ever changing through the large number of abilities that moved combatants around the board, it kept things engaging for the players even during someone else's turn. Some of my players liked it, especially the min-maxers who liked the extra level of control they could exert. Eventually, the combats became too slow and ponderous and we moved onto other games.
With 5E coming out we decided to give it a try and are enjoying it, especially the speed of combats and overall game-play. However, I have decided to purposefully keep combats in the theater of the mind instead of resorting to maps and minis. While I love the look of minis and believe it helps with immersion by letting the players "see" what their characters see, I also feel it overall slows down game-play. Setting up maps and minis takes time. Players seem to dither longer as they want to optimally move their mini on the map. Math is hard when calculating movement rates/speed.
Thus I have been keeping things as narrative as possible. I have even forgone simple things like movements rates by and large. Instead of saying "the enemy is 40' away", I say "the enemy is 2 rounds of movement away, though you can get there this round if you run, but then you can't attack". I feel this takes away the math ("my speed is 30' and if I run..."). I don't really bother with the math, but rather am more narrative.
And it is hard for my players to play with this more narrative/theater of the mind approach. They seem to instinctively want to go tactical on me. They want to maneuver to avoid attacks-of-opportunity, even though it only activates when they leave the threatened area (as they learned last night night they can move into melee and then circle the enemy as long as they stay within 5') - basically they are trying to avoid something that no longer exists in game mechanics. They want to flank even though there is no mechanical advantage for doing so (I have decided to not use the optional flanking rules). They want the fleeing enemy to be blocked by the mage that was near the exit door (even though she just got shanked down to 1hp in 1 blow the round before and was trying to stay safe).
Last night, one player's character moved up next to an enemy simply to gain the the game system mechanic of being engaged with them (he couldn't attack since he had to spend an action moving to reach the enemy). It wasn't a case of "I move to keep the enemy busy and distracted" - it was a case of "I move so I can get an attack-of-opportunity if the enemy tries to flee and so the rogue gets an advantage to her attack since I'm in base-to-base with the enemy".
There is a disconnect between the narrative and the game mechanics going on here. However, this is mostly because the min-maxer of my group looks at everything from a game system point of view rather than a narrative point of view.
Basically, min-maxers seem to love tactical maps because it allows them to control the fight in another way. By going more narrative they lose some of that control. They want the enemy constrained by the map and a theater of the mind tends to be looser than that. Some of my players are having a hard time readjusting to the new format of theater of the mind. We briefly discussed the use of minis and they verbalized that they were fine with not using maps and minis but we'll see how it pans out over time. Near the end of 4E I was trying more off-the-grid combats and they worked somewhat so my players have seen it before (and they are old 1E games so it is not a new concept). Still, it will take some getting used to for them.