the nato and un mission, which canada joined in the un capacity first and the nato capacity second, was not intended as an offensive mission to wipe out the taliban so much as it was intended to hold the capital and rebuild the government. the problem that the un sought to address was not the elimination of the taliban but the absence of a government in kabul. it was primarily a peacekeeping mission.
there were combat missions under american direction but they weren't the reason that most countries went to afghanistan and many were reluctant to participate in them.
while the terrain is difficult, and that was a reason that many countries were reluctant, it is unlikely that the taliban could have withstood a direct, full assault by nato countries, and many observers pointed that out at the time, with comments like that nato is fighting with one arm tied behind their back. one justification i heard by nato at the time was that nato found it more useful to study the taliban by intercepting their communications with the intent to subvert and co-opt them than it did to just blow them up.
there was no proxy group like the kurds in the region to do the heavy fighting on the ground.
that doesn't mean people weren't maimed or injured in the defensive capacity, but the fact is that they weren't there to conquer the country, and that is why they didn't.