In my country, 30-40 years back, people who needed a watch were those ones who travel regularly. And travel was mostly using public transport, trains and planes. Most or all of it operated using a 24h time. That button was very useful. Compare that to the mute/silence/DND physical button in iPhones today.
Also people who worked in confined spaces who wouldn’t know if it was day or night outside after a days job. My father who worked in an oil rig in Abu Dhabi used one. He gifted me one.
This was 1998.
How about just leaving it on 24h time all the time?
Yes but why not just always use 24h time (or 12h if that’s what you like).
It’s a little strange that a dedicated button would be needed to switch between them, especially when the math to convert between them is so simple.