As has been mentioned, scopes help not *just* with distance shooting (although they do help with that too) - but principally with low light shooting and target ID at most any distance.
And as mentioned, the answer depends on the skill of the shooter, the eyes of the shooter (how good or old), and the type of iron sight used. But very generally, you might could say that someone with older eyes (over 40) like me are comfortable shooting a whitetail deer sized vital zone (10" across let's say) with typical "buckhorn" sights, and average skill, at only around 100-125 yards; maybe 150 (but less in low light!). But I am comfortable with a good scope & rifle shooting a whitetail at up to 275 yards or more under the right conditions (good rest, very little wind), and that's even in low light. So that's a very significant difference for me, that a scope adds to the practical hunting range (about TWICE). Yes, I would probably hit the deer in the vitals and kill it cleanly with irons at even around 200 yards, but I just wouldn't feel comfortable trying it.
With a larger kill zone, such as an elk, just add around 30-50 yards to all ranges, irons or scopes.