First off, in 4e, in combat healing was a major element. The baddies and the PC's had roughly similar starting HP pools. Give or take, but, not too far off. Where the major difference lay was in the fact that 4e PC's could heal (and heal a LOT) in combat and could mitigate damage as well. And this was necessary - 4e combats were intended to be pretty lengthy affairs - 8+rounds wasn't all that unusual for a combat. In order to keep things going that long, you needed in combat healing. But, 5e doesn't work like that. Combats are much shorter and, generally, other than standing someone up from 0, in combat healing isn't much of a thing. How much healing do you really need when combats only last 3 or 4 rounds?
Secondly, battlefield movement is much less of a thing in 5e. Not because we don't use a battle map, at least, I certainly do. But, pushes and shifts are not such a big deal. You can dance around an opponent without drawing OA's and, even if you do draw one, it's usually not that big of a deal. Again, the monsters aren't dealing that much damage on single hits. Eating an OA doesn't radically change the combat too often. Granting bonus movement is also not such a big deal when PC's can move attack and then move again in a single round. IOW, just with the existing 5e rules, combat continues to be pretty fluid, featuring lots of movement anyway. Adding in a PC that adds to battlefield movement is largely just gilding the lily. Plus, since things like grappling and monsters dumping on status effects aren't anywhere near as big of an issue as well means that you don't really need to mitigate these effects either.
What's really left over? The more I play 5e, the less I think 5e needs a warlord.