Give me an example of how the warlord was defined by 4e traits.
Oh dear, you're going to make me pull my dusty 4e books off the shelf, aren't you. Alright then.
Looking down the 1st level at-will abilities, what have we got? Give an ally an off-turn basic melee attack, that's very 4e and only works because basic attacks are standardized. Give an ally a numerical bonus on their next attack, that's the 4e numbers game there. Deny an enemy the ability to move without provoking an Opportunity Attack, that's 4e positional play at work. And give an ally the ability to shift 1 square, that's 4e off-turn actions and positional play again.
Skimming further down the list it's mostly following those themes. Give allies a numerical bonus to this or that. Allow allies off-turn movement and attacks. These are deeply 4e things that have been toned down or eliminated in 5e. There's some fairly standard healing tools, but others that tie into 4e specific concepts like ongoing damage.
As a Warlord fan, would you really say that a 5e Warlord that has roughly a Battle Master Fighter's ability to do those things is really a Warlord? Of course not. What you loved about the Warlord is the ability to control the battlefield like a chess board, sliding your allies around and pushing them into making attacks. Those are
not things 5e does because 4e went heavy on the tactical skirmish gameplay and 5e does not.
5e doesn't want people to slow the game down by making players regularly engage with off-turn actions and movement. 5e doesn't want to complicate the game with lots of fiddly little attack bonuses to track, or penalties applied to the NPCs. These are the Warlord's stock in trade, and they're not part of 5e's catalog.