A number of high-fatality fires in structures over the years have involved a fire in one part of the building using an open stairway as a chimney to both fan the flames and to spread between levels. That's part of why the US stairways generally have fire doors that will "fail closed" at any fire alarm - by having the doors all closed, and (often) a ventilation system that overpressures stairwells somewhat, you have a clear space to evacuate, and, at worst, doesn't actively help the fire.

The alternative is that as a fire progresses on a lower level, the hot gasses find an open stairwell and head up, quite rapidly. The air coming in to replace this is effectively a forced draft for the fresh fire, and the hot gasses going up rapidly end up hot enough to start igniting things on other levels, in addition to making the stairwell totally unusable for evacuation. If you're unlucky, a well placed stairwell with a skylight that rapidly breaks from heat can turn a first floor fire into, quite literally, a very effective furnace with exceedingly poor containment.

This effect, unfortunately, has been demonstrated at great loss of life in various school fires and such over the years. https://en.wikipedia.org/wiki/Collinwood_school_fire is one such, but there have been quite a few others over the years as well.

As much as it may be architecturally unpopular, the stairwell requirements in US buildings are one of those "written in blood" regulations that have very good historical evidence for why they exist.