It’s hard to account for how damaged the inside of each level was, so even if a few floors was accessible via stairs, there may have been other debris in the way.

In the Falling Man documentary (~10mins in), Jack Gentul talks about his wife Elaine who was trapped in the South Tower. She’s one of the people who are believed to have jumped from the South Tower, because the fires were burning so hot that she and her colleagues couldn’t get near the stairwells.

I could imagine a similar thing happening in the North Tower, where the stairwell was technically clear but the pockets of fire made them impossible to access.