There are a lot of globally successful taiwanese companies, TSMC is obviously the most prominent but then you got companies like Giant, Acer, Asus, BenQ, zyxel, gogoro, etc.
Taiwan is doing pretty good actually considering their size, I doubt they are doing any worse than e.g. Australia which is of the same size. Throwing in the fact that Taiwan is not officially recognised either and the lack of FTAs, they are doing very well.
They are good companies, but honestly if you go to Europe or US with those names I doubt 1 in 10 people would recognise them. TSMC like Foxconn has a significant part of their operations and factories in China so I m saying Taiwan is very much intertwined with China and China has a lot of bigger cities that can act as finance hub. Mind you I love Taiwan and visit the place at least 3 to 5 times a year but I cannot deny the lack of development since I started doing business there more than 10 years ago.
Taiwan will trot along just fine but it is definitely not a "dragon" and with geopolitical issues, restricted currency, massive spending on defense it is hard to see it as a finance hub in the near future.