In other words, why haven't there been "______ beauties" for all kinds of products in Taiwan? What made betel nuts special? Wikipedia seems to cite intense competition, but it's not like the betel nut market is the only competitive one out there.
How it happened is that it kinda just happened. It's not that it began as scantily clad women. The original "betel nut beauties" were much more modestly dressed. The same question can be asked for the funeral pole dancers; There was a performance for the deceased which over time became what it is today, but didn't just appear out of nowhere.
The origin is traced back to the Xiè family in Cǎotún Village just south of Taichung. They had a betel nut stand in the early 1970s at which the three daughters of the family (Xiè Xiùzhū, Xiè Xiùhuā and Xiè Xiùlán) were employed. Teenagers at the time, the daughters are credited with attracting a lot more customers than competing businesses. Customers were enamored enough to send them gifts and attempt to court the girls. Their position in the history of the Betelnut Girls culture is pretty well cemented, and you can find the same story about them told in any number of sources.
Later on in the 1990s a television variety act of singers Cáo Lán and Yáo Dàiwěi became quite popular and was credited with furthering the culture of Betelnut Beauties. You can see one of their more well known acts here. You'll notice their style of dress is still somewhat conservative there.
There's more than can be said about the history of the development, but the answer to your question is a lot more mundane that what you might be expecting. The target market has often truck drivers and people of a lower socioeconomic background, a market for which the gradual progression to what you'd see in more recent years was perceived to be a significant economic benefit, but not at all something that happened overnight. If anything it's been going the other way, as in the last 15 years regulations have gotten tighter as far as government imposition of dress codes. And by no means is the scantily clad clerk a requirement, as many betel nut stands throughout the country have regularly dressed sellers.
Point is, the same can be said for KTV girls, or the Taiwan Beer girls you see at bars. The undressing is something tied to the standards of the times and the nature of the work.