I do not think you understand the idea.
The Eldritch Knight is a subclass of fighter which represents a Fighter/Wizard.
I was suggesting the Warlord as full class then causes the Battlemaster to retroactively be a subclass of Fighter which represents the Fighter/Warlord.
Now the idea may not be awesome but that is the thought
Yes, you take the Battlemaster mechanics.
And you make the Warlord that times 3, minus Fighter baseline.
EK have very few spell slots (Wizard fuel) and a restricted set of Wizard abilities to pick from.
BM will have very few Warlord ability fuel (maybe superiority dice), and have a restricted set of Warlord abilities (its maneuvers) to pick from.
On top of that, Wizard has features that enhance its spellcasting, both core and subclasses, that the EK lacks. The EK has a handful of spellcasting+melee hybrid abilities that the Wizard lacks.
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Using that approach, you'd rename LEADERSHIP DICE into Superiority Dice, and the "tier 1-1.5" abilities would be similar to the battlemaster abilities from level 1 to 20. At level 20, a BM has something like 6d12/short rest; the warlord could have similar power scale by level 7.
EK has 1st level spells at 3, 2nd at 7, 3rd at 13 and 4th at 19.
BM has 4d8 dice at 3, 5d8 at 7, 5d10 at 10, 6d10 at 15 and 6d12 at 18.
We then scale for a "Pure Warlord" and we'd get something like:
4d8 at level 1
5d8 at level 3
5d10 at level 5
6d10 at level 6
6d12 at level 7
Now we could refactor further.
The Warlord could get at-will or per-turn superiority dice right out the gate, the BMs "per short rest" dice being an inferior version of them.
Level 1: 1d6 at-will superiority die per turn
Level 3: 1d8 per turn
Level 5: 2d10 per turn
Level 7: 2d12 per turn
Level 9: 3d12 per turn.
then level 11+ abilities would be a phase change. (Refresh at end of turn, because Warlords are all about that sweet off-turn boosts. Only the dice you don't burn on other people end up coming back to you, to mop up on your turn).
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This isn't making a BM into a full class, nor is it making the BM a subclass of Warlord.
It is using the structure of the BM and retroactively making the BM a hybrid Fighter-Warlord to make the Warlord feel more naturally part of 5e.