Here is some of the warlord flavour text from the 4e PHB (I've only surveyed powers up to 5th level, for reasons of time and space):
You call out to a wounded ally and offer inspiring words of courage and determination that helps that ally heal.
With a shout, you command an ally to attack.
You slam your shield into your enemy, bash him with your weapon’s haft, or drive your shoulder into his gut. Your attack doesn’t do much damage -but your anger inspires your ally to match your ferocity.
You trick your adversary into making a tactical error that gives your comrade a chance to strike.
Step by step, you and your friends surround the enemy.
With a calculated strike, you knock your adversary off balance and grant your comrade-in-arms some protection against the villain’s attacks.
You land a ringing blow against your foe, inspiring a nearby ally to strike a blow of his own.
Like a leaf caught in the autumn wind, your foe is driven by the flow of battle. Your fierce attacks force him to give ground.
With a calculated blow, you leave your adversary exposed to an imminent attack from one of your closest allies.
Honorable warriors never fall!
Under your direction, arrows hit their marks and blades drive home.
No matter where your foe turns, one of your allies is waiting for him.
You lead the way with a powerful attack, using your success to create an opportunity for one of your allies. Each of your comrades in turn seizes on your example and begins to display true teamwork.
Your presence is both a comfort and an inspiration.
A timely critical hit affords you the opportunity to rally a wounded ally.
With a sharp wave of your arm, you direct one of your allies to a more tactically advantageous position.
You convince yourself or an ally to shake off a debilitating effect.
With a snap series of commands, you keep your allies in formation and well defended as you assault your adversary.
As you strike, you shout a fierce war cry that heartens a nearby ally. He immediately attempts to shake off whatever condition troubles him most.
You leap into the fray with a wild, whirling attack - but your movements are carefully calculated to distract nearby enemies and give your allies a chance to move into position.
One convincing cut is all you need to reveal the enemy’s weakness and spur your allies into finishing him off.
You will not be denied victory! A determined strike lifts the spirits of your beleaguered allies and restores their fighting spirit.
A well-placed strike catches your foe off guard and allows you or a nearby ally to shake off some effect.
You use weapon thrusts, lunges, and parries to hedge in your adversary, preventing him from moving away from you.
Here are the verbs that relate the warlord to his/her allies:
inspire *4
comfort, hearten, lift the spirit, rally, spur
lead the way
convince
command *2
direct *2
I'm not seeing a very strong implication that the warlord is the party leader - of 24 powers, 2 allow the warlord to give a command (which the other PC may or may not comply with) and 2 allow the warlord to give direction (which the other PC may or may not follow. I don't see how the flavour of this is any different from 5e's existing battlemaster.
We mostly have the warlord inspiring, heartening, rallying, spurring on, etc. That doesn't imply that the warlord is the party leader. Nor does it imply that the other PCs have any particular relationship with the warlord, other than being open to his/her heartening or inspiring words. And, again, if a player doesn't want his/her PC to accept the buff, why is s/he forced to?