Every large building in the last 100 years has been built with multiple integral fire-safe paths of egress for the very reason that a path should be available if one is blocked. The design of buildings is very much conditioned on tables in the fire code about how many paths of egress, how large they must be, and how long they can be based on how many people need to be evacuated. (Not to mention how many hours of fire each door and partition must be designed to resist.) It's kind of a PITA. And it works very well.

External fire escapes are merely the retrofit allowed to old single-stairway buildings to get them to be vaguely as safe as a modern building.

In San Francisco, there's a bit of a push right now to re-allow single-stair design ("Single Stair Reform") for certain buildings (eg up to 4 or up to 6 stories). Requiring two stairways makes sense from a fire safety perspective, but it's made it incredibly difficult to cost-effectively build medium-size buildings on oddly-shaped lots.

It's tradeoffs all the way down!