aramis erak
Legend
Meh. D&D was never "meant to be theatre of the mind." I question whether that was even a serious intent of 5e.
you should listen to Dave Wesely discussing Braunstein... It undercuts your argument heavily. As does Dave Arneson's comments on how dungeons were run. And Gygax's comments. Anyway, the gist is that Braunstein was played more as a LARP than as a minis wargame, even tho' it was nominally a minis wargame. And Braunstein lead Arneson to Gygax.
Now, Professor Barker is shown using minis on 3d terrain... but many of Gygax's players note that minis were not used for combat, and that, while the minis combat rules were legit, weren't used in Gygax's play except for actual large scale engagements. (But note: I've read reports of 20-player games, with 3-5 henchmen and 1-2 characters per player on some of the adventures, in some of Gygax's early sessions.)
Likewise, I've run TOTM semi-RPG sessions of Car Wars (SJG) and Warhammer 40,000 Rogue Trader (the original GW one) and Inquisitor (also GW)... it's quite doable to use minis rules in non-minis play.
As for 5E, Mearls explicitly stated that being well suited for TOTM style play was in fact a design consideration in one of the 5E-playtest era posts.
Now, there have always been some groups that do more boardgamish play, and some that are mostly TOTM, and a few that are pure TOTM. [MENTION=82779]MechaPilot[/MENTION] 's list of reasons why TOTM groups might delve to minis is pretty good.