The problem is that vast majority of Taiwanese would never pay NT$500 per hour for a babysitting service, since they rely heavily on family to look after children when the parents are working or out. The only people paying for such a service are foreigners without family in Taiwan, rich people who don’t care, and a very small group of Taiwanese with no family able to help. You also have to consider that most outcall babysitting jobs are likely only available for a short period, perhaps around 7 to 11PM, meaning that anyone becoming a professional babysitter can only work for a few hours a day, so they have to charge more in order to survive.
AFAIK, you have to be licensed to babysit babies, my wife’s friend babysits a few infants in her home every day, almost like a private nursery, and she said that it is not a straightforward process to get licensed. She has a degree in early child care, and also had to do an exam.