The Warlord was one of my most favorite developments in 4e and the visceral response to it by other people just makes me scratch my head.
but it's also an effect of 5e where it's a magic exception system. it's openly hostile to non magical answers to problems.
I bet if warlords lightly opened up the possibility of magical (not spells) effects, things would flow a lot more smoothly for people.
I.e.
While any intelligent beast can predict the trajectory of a rock flying though the air, and any intelligent humaniod can make and communicate dinner plans, the Tacticians take that to an whole new level. They are able to predict enemy an ally movements alike and devise stratagems that many call prescient. Fortunately for the rest of the world, too much analyzing will tire the warlord out.
How a Tacticians achives this remains a mystery even to themselves. Some say there is a divine spark leading them to a destiny, other say they can see the weave of fate or are imbued with divination magic, and others insist that it was just years of hard study and endless hours think of the best stratagems, honing their minds into a razor sharp edge.
Tacticians are nearly always draw to adventure, as mundane life becomes too predictable and boring. Having often played and beaten everyone they know in any strategy game, they often seek out the challenge of battles in order to stretch their abilities to the limits.
Good aligned Tacticians see themselves as protectors and guides. Using their abilities to increase the total amount of good in the world. Evil aligned Tacticians may even start wars if they can't find any to join, playing with lives as pieces on a game board just to alleviate their boredom. Though any good game player knows that even a pawn can be value if used correctly.