Actually, yes. (Well, the third one did.)
The South Tower had one remaining stairwell survive impact and 18 people were actually able to evacuate from above the impact zone, which is actually pretty impressive when you consider that the impact was on floors 77-85, and the people who called emergency services were told to stay in place. One of the survivors was actually only 20 feet (6 m) from the left wing. https://en.wikipedia.org/wiki/Stanley_Praimnath
That being said, a lot of fire codes and related legislation had to be updated in the wake of 9/11. Among the many other dumb things:
* the stairwells were all extremely close to each other. In the North Tower they were 70 ft (21 m) apart and in the South Tower they were 200 ft (60 m) apart, which is probably why one stairwell survived in the South Tower and none did in the North.
* stairwells were only surrounded by drywall instead of concrete, which is another contributing factor to why so many of them were rendered inoperable. If you're not familiar with drywall, you can literally punch a hole through it with your arm.
* stairwells were built with a 44 inch width because it was assumed that the average person had a shoulder to shoulder width of 22 inches (55 cm). This slowed down evacuation a lot.
* the fire code was incorrect. the building was only half full but took much longer to partially empty than a full evacuation of the full occupancy tower was projected to take. so codes were revised.
* there were not enough stairwells according to code. but how might this be? well, the owner and constructor, the Port Authority of New York and New Jersey, is a federally created entity, and so is not actually subject to local fire codes. (This last point wasn't actually addressed; they're still not actually required to follow NYC fire codes, but they did at least do so for the new iteration of the towers.)
* In a previous attack on the WTC, people were evacuated from the roof, but since that incident the roof doors were locked to prevent base jumpers from gaining access.
https://www.history.com/news/world-trade-center-stairwell-de...