If I decide that my Ranger has a problem with authority (a pretty common trope for adventurers), and that's why he is in an adventuring group instead of in the military, then someone else bringing in a Warlord character is going to be a problem.
I think you are overstating things. (Or, perhaps, overgeneralising from your own idiosyncratic preferences.)So you do not approve of my character concept and I must change it to fit into your idea of a team?
This just illustrates the problem with the Warlord.
One consequence of expressing inspiration mechanically is that it doesn't impede any other player's agency. If the warlord player uses an action which allows another PC to charge and attack an enemy (say, a balrog), then (i) the other player gets to choose whether or not his/her PC performs the charge, and (ii) if s/he does choose to do so, no agency is lost, because the warlord has amplified the action economy, not used it up.
Similarly with hit point recovery, or granting some sort of bonus or reroll to a die roll - this doesn't interfere with anyone's play of his/her PC, and if the player doesn't want to take the buff (on the grounds that his/her PC would not be inspired) s/he is not obliged to. (Eg in 4e, the player can choose not to spend the healing surge.)
None of this implies that the player of the warlord is empowered to direct the other players how their PCs should act or expend their own resources and their own action economy.
On the general point: there are many character ideas that can upset other players. Eg I roll up a paladin of Bahamut and you roll up a cleric/assassin in service to Wee Jas. If we both bring these characters into the game, are you going to accept my Lay on Hands? Am I going to accept your Bless? Working these things out, either at the meta-level when building PCs or by seeing how it unfolds in actual play, is just part and parcel of playing a party-based RPG.