Maybe. But, you can't have it both ways. You can't on one hand tell Warlord fans that they already have everything they need to make a warlord in 5e, simply use the multi classing rules, and then on the other hand complain that the things that make something a warlord are so over powered and bad that they shouldn't be in the game.
Which is it? Can I make an approximate warlord in 5e or not? And, if I can, then obviously it's not a problem for all these elements to exist in a single character. Thus, creating a class devoted to those things wouldn't be a problem. It's simply streamlining a process and cutting away cruft that shouldn't be added onto the character (why is my warlord singing? why is my warlord a better swordsman than the paladin or ranger? why is my warlord casting spells? why does my warlord have a divine oath? etc)
I started this thread to try to identify the niche that warlords can fill. I'd say that the following niches aren't really necessary:
- Forced movement - just not a real thing in 5e
- In combat healing - it was never really necessary for a warlord to be a healer anyway, IMO
- Status mitigation - so few monsters have ongoing effects, that it's just not that needed to have a class focused on dealing with it.
However, I do see several niches that a putative warlord can work with:
- Action economy management - adding actions/attacks. This already exists in the game and can be easily balanced. Both Battlemasters and Beastmaster Rangers provide the mechanics - give up an attack to allow an ally to make an attack with some bonus.
- Out of turn actions - this is a big one. Being able to allow another character to do something out of turn is a primary focus of a warlord class
- Buffing the party - easy one to balance. If clerics/druids can cast Guidance/Resistance at will and grant a d4 to skills and saves, then another class doing the same thing, or perhaps granting advantage, isn't breaking anything.
Those three elements are enough to hang a class around. I'd probably go with a rogue chassis, replacing sneak attack which increases every other level, with a small suite of at will effects which increase, probably on a similar curve. The two subclasses focus on Int or Cha respectively and the Int warlord focuses on adjusting action economy while the Cha warlord focuses more on buffing.
I'll have to spend some time writing this up.