I've had a different experience of the Taiwanese elementary education system than most - extremely positive.
My daughter had always had problems fitting into school, starting as a five year old back in her home country. I'd heard all the stories of the perils of the Taiwan education system and was very very worried about what I was bringing her to. She was nine years old at the time, and spoke no Mandarin. After some hunting around, I decided on a small "mountain" school. These schools are still part of the govt system. Because of difficulty getting a sufficient roll of children from their local area, they often expand in creative ways to fill a niche, and like to take students with "special needs", who are eligible to be counted as one and half, or two students, for funding purposes. Hence, schools can continue to operate with very small class sizes. Cool!
My daughter was a special needs kid, on account of her lack of Mandarin.. which meant that she got lots of free one on one hours with a lovely patient teacher who took her walking in the mountains when study all got too much for her. There were only 13 children in her grade! So she got to be on the swimming, baseball, dodgeball, athletics, football teams for three years in a row. At school shows or sports event, every child in the school had a turn and received support and applause. The kids LOVED their school. They were proud of it, happy to clean it and take care of it - (the notion of deliberately harming it in some way would be unthinkable) and they treated their teachers with respect and affection. We LOVED the concept of half days, and she thrived with the very sensible regime of ten minute breaks to run around madly between every fifty minute class. There were student centred creative and positive solutions put in place to help her when her behaviour was unacceptable. This environment completely turned around my daughters bad attitude towards school, and she learned so many positive things from it that will stay with her for life.
I will remain forever grateful to the Taiwanese Education system for this!
When we arrived, I couldn't speak any Mandarin either, and the school was incredibly considerate - always provided their English teacher as a translator for me in meetings.
This particular school had about 30% "mountain" kids, and the rest bused in from all parts of the city. Many of them were foreign born Taiwanese, who needed time and extra help to pick up their Mandarin language, or reading and writing skills. Many had parents who just didn't want their kids to have to start coping at such a young age with the pressures of homework and exams that the city school present. The school responded accordingly, and was in many ways fairly "alternative".
My daughter arrived there speaking no Mandarin. She was conversing freely in basic Mandarin within six months, and was fluent in a year. It took her longer with reading and writing of course - and this would have compounded into more of a problem for her if we'd continued in the local system.
I would highly recommend it as an option for kids up to the age of 12, especially if they're only going to be here a year or two. My feeling is (and I'm also a teacher) that what they learn about learning itself, and the cultural and language benefits, far outweigh the risks of "missing out" on something in their English language schooling, when they return to it. Particularly if they're already reading and writing in English, and that can be supported at home. If you can read and write, you can always catch up with the facts you need for exams.
If you're staying longer, it's more of a dilemma, because you have to think about what your children are going to do AFTER elementary school. Middle high is a whole other world.. of weekly tests, huge class sizes and only ONE way to succeed. If your kids aren't cut out for this, (mine definitely wasn't!), or if their Mandarin reading and writing skills aren't sufficient, as is almost guaranteed unless they start here at five or six, then you've got a problem. Get up to speed, Go home, or Hope for windfall to pay their International school fees.
Those interested, the school my daughter went to is Datun Guoxiao, ten minutes up the mountain from Beitou. There's a free school bus that picks up from the Beitou MRT. There are a couple of other similar schools that I know of, that also have foreign students, in the YMS area.