As for what traits a 22nd century captain should have, I'm not sure. I think diplomacy skills, a tolerant outlook toward other species, adaptability, scientific curiosity, some basic ship technical know-how, military toughness should all be in the mix. IMO, it's debatable how much any of these traits Archer possessed.
While far from perfect, Archer possessed all of those traits, or acquired them eventually:
diplomacy skills – The Breach, Cease Fire, The Council/Countdown/Zero Hour, Babel One, United
tolerant outlook toward other species – Unexpected, Sleeping Dogs, Cogenitor, really, any episode with aliens
adaptability – Civilization, Fallen Hero, the whole Xindi arc, it’s one of his defining characteristics
scientific curiosity – Strange New World, Breaking the Ice, Cogenitor, First Flight
some basic ship technical know-how – Singularity (piloting), The Crossing, First Flight, Damage
military toughness – Silent Enemy, Fallen Hero, The Expanse, the second half of the Xindi arc, the Augment arc.
In addition, he had compassion in spades, and an unwavering loyalty to his crew.