OK, to me that is incredibly easy to do in 5e. You basically just have to take some options off the table, done. Where are you having the hang up?
"Some" options?
You're left with 2 classes - fighter and rogue. That's it. The half caster classes mean that the game features repeated spell casting every single combat. How do I know? Because when I ran my Thule campaign, I allowed 1/2 casters like Rangers and monks, and every single encounter featured magic. Social encounters featured magic. Exploration encounters featured magic. Just like standard 5e, even with 1/2 casters, the PC's have a MOUNTAIN of magic available to them.
So, basically, I would have to strip out so much of the game, that it's just not worth it anymore. Anyone who wants to play a more tactically interesting game being restricted to fighters and rogues and 5e's ruleset is bored out of their minds because fighters and rogues in 5e do the same thing over and over and over again. They're the "simple" classes. That's their attraction. I've been told that repeatedly enough.
You want to do anything other than straight up attack in 5e with a fighter? Ok, well, there's no rules for it, so, now we're back to playing Calvinball. I want to sweep my sword through the sand and blind the three bandits in front of me. How do I adjudicate that action? 4e would be simple. 5e? There's no "maneuver" system in 5e. Which means I'd have to bolt that on or constantly have to make stuff up.
Heck, I want to throw my sword at someone, Conan style isn't handled by the system. Never minding the aforementioned chase rules.
So, yeah, it failed utterly to do what I wanted it to do. The players hated it because they found it unrelentingly boring as soon as dice started dropping.
If I were to do it again, 5e would be the last system I would try to use to run that style of game.
But, apparently, this is offensive to talk about because 5e can do everything and any failure must be entirely my fault and nothing to do with the system. So, I guess I'm just not as good a DM as the OP. C'est la vie.