You are brutally missing the point.
I just like that turn of phrase.
Effects are balanced (for the most part) based on uses per day. A melee attack is infinite because there is no factor stopping a PC from using it except opportunity.
Yep, and a key to balancing limited-use abilities is how limited those uses are compared to opportunity to use them. A top-level caster in 3.5 might have had as many as 8 or 10 of his top two spell levels available another 30 or 40 lower level spells, plus as many scrolls as he felt like making and hundreds of charges in wands. He might have as many as a thousand 'limited' uses of magic to use as the opportunity presented itself during the day. A day that might have been 4-6 'rocket tag' encounter of a round or two each, or even only one such encounter. Even looking at his top two spell levels, he's really facing almost no resource limitation at all.
5e casters aren't nearly that bad. If you stick to the 6-8 encounter day, and assume 2-5 round encounters, even a 20th level wizard with 22 spell slots can't blow one every round. At worst every-other round, though, and then cantrips the rest of the day.
So any warlord power that doesn't cost a token to use (be it point, die, slot, or rest) needs to be balanced as if it will be used every round, since there is no "penalty" for not using it.
And, if the warlord also has other abilities that are limited-use (token mechanics or otherwise), the way casters have both slots and at-wills, then the relative power (and variety) of cantrips might be a better guide than the high-DPR-only benchmark established by the other non-caster sub-classes.
2.) Is the power a better use of the action (or bonus action) than anything else he can do "for free"?
Interesting question. For a Fighter, for instance, attacking is better than anything else he can do (basically everyman stuff like the Help action or a check), hands-down. Is that problematic? Does it make extra attack 'too powerful?'
3.) Is the power the best use of the recipient's "reaction" per round?
This comes into the same uncertainty that you face when deciding whether to expend a resource. You know what you can do with your reaction - and can do more with it if you cast spells as a reaction, or use Protection Style, or whatever - but you can't know for sure if it'll be called for. That makes expending the ally's reaction a fairly heavy limitation on the ability.
At a very basic level, the at-will ability to grant an at-will ability is the most powerful at-will ability in the game.
On another, it's also the most trivial, since it adds nothing new to the party's repertoire.