For the answer of why a specific button is used for Popcorn, I recommend looking at this discussion from Reddit which has this to say :
Many microwaves nowadays, except for very basic models, will actually
have a humidity sensor built into them. They measure the moisture
content coming off of your food to determine when it's done, because
microwaves work by exciting water molecules in your food. The
different food buttons basically narrow down the expected range of
humidity, because if you think about it, your popcorn has a much
different moisture content than Grandma's turkey dinner.
That said, the microwave has become synonymous with the making of popcorn and since popcorn does have the same content and similar moisture across different brands, setting up a single button to just do the job is just another selling point about what all the Microwave can do and how it can save time.
Interestingly, popcorn was the first item ever heated in the microwave if this quote from History of Popcorn is true
Microwave popcorn -- the very first use of microwave heating in the
1940s -- has already accounted for $240 million in annual U.S. popcorn
sales in the 1990s.
Note : I'll update this answer with a more scientifically driven response if I can find more data to back it up rather than relying on some poster in Reddit.