Principly I agree that it's not a must to go abroad to better learn English, but you need to know the correct way of learning it in a non-English environment, or you can never learn well. I'm 52 now and have never studied or lived abroad in my life, but I have had no problem to interact with my foreign customers in fluent English writing and speaking in my trading career for 29 years by now.
The weakest part in learning English without going abroad is about speaking. Apart from practicing it with a headset, listening to English radios, and watching English movies/videos, you need to enhance this part by grabbing as many opportunities as possible to practice it with any native speaker who lives in or visit Taiwan. Apart from foreign teachers in schools, you have chances to meet foreign tourists/residents on the street, the missionaries in the church, and probably those foreign customers at your work. Joining cram schools is an efficient way but it's a bit costly. If possible, you may seize a chance to make language exchange arrangement with someone who comes to Taiwan to learn Chinese.
The second weakest part in the same regard is about those slang expressions. From books or internet you can always get a big collection of American slang pieces, but you can get little chance to practically use them in your daily life because even those American visitors won't talk in slang way when they are in Taiwan. However, it did not bother me for not learning them, because slang English is spoken locally in America only. If you are not going to live in America, it won't be a big problem.
As to writing, learning it here in Taiwan makes no much difference from doing abroad. You can take good advantage of the internet resources to improve your writing. In addition to your school learning of vocabulary, phrases, and grammar, the most efficeint key is "read, read, read" and "write, write, write". English textbooks, dictionaries, newspapers, magazines, novels, and other publications are what you have to often approach. The internet resources cover them all. If possible, communicate with your foreign friends in English more often. And of course, spare your time to come to and utilize ECT chatrooms and forums. There is no short cut in learning to write but continuous practice. Of course, getting proper guidances from the right people is what you always require, too.
This way, if it is not convenient for you to go abroad for English learning, just do it locally in Taiwan.