Well, eventually. Boromir, with multiple arrows piercing his internal organs, manages to kill half a dozen or so of the Uruk-hai before breathing his last breath. It's played like a devastating loss for the fellowship, but on Saruman's side they had to have been realizing that if that kill ratio kept up, the orcs and goblin-men were going to need to step up the fuckin'.
Which, to be fair, they totally did.
But OK, there were only a few Uruk-hai in that scene, and maybe they were tired or something. So in The Two Towers, the real Uruk-hai army shows up, 10,000 of them at the Battle of Helm's Deep ...
"So, um ... is there, like, a plan? We aren't just going to charge right into their arrows, are we? Guys?"
At which point rows and rows of them are mowed down by a tiny, ragtag group of random untrained dudes the good guys pulled off their farms. The massive, overwhelming force of specially bred soldier-monsters is held at bay for hours before they resort to suicide bombing the fortress. This works briefly before reinforcements show up for the good guys -- reinforcements of regular soldiers, not specially bred super-soldiers -- at which point the Uruk-hai flee for their lives and are punched to death by trees.
Trees on Thorazine.