In theory a player can certainly role-play a pure fighter as a leader and strategist, sure.
In practice, in my 40+ years of gaming, I think I can count on one hand the number of times I have seen a player lean into that archetype. Why?
1. Survivability trumps role-play -- players would rather boost Dex or Con than Int, Wis or Cha for a fighter. In 3e I saw a smattering of Int 12 or Int 14 fighters who wanted skill points but that didn't really change their narrative.
2. Players usually choose fighters to experience the joy of running a PC that is personally effective at combat. If they want to play a support role they turn elsewhere.
The narrative choice of 'how do I want to play my fighter' usually comes well after the character is built, and is both informed by and constrained by the above.
I have played battlemaster fighters -- one of my favorite classes -- but they are still fighters and not intrinsicially leaders because the class abilities don't support that narrative well. The only martial PC in recent memory that I chose to play as a leader / strategist was a 3e Knight.
So my own feeling, based on personal experience summarized above, is that carving out the leader/strategist narrative from the figher and giving it to a new class, is not taking anything at all away from the fighter in practice.
It's like giving away that drum set in the garage that you never play, but hold onto because you might want to join a band, someday, after you learn to play the drums.
