I’m not expert on this, but I think the last statement I quoted from you is the main thing to remember. Whether or not the capital city of this island should be spelled “Taibei” (according to Hanyu) or “Taipei” (according to something else) is a moot point. Whether the issues behind romanization in Taiwan are silly and intricate doesn’t matter either. For so long, internationally, it has been spelled “Taipei.” Therefore, in most context (unless you are writing it personally) it should be “Taipei.”
The same is true for people’s names. From what I understand, for a long time Taiwanese were able to choose the romanization of their name on their passports. (Am I wrong in that?) That is why you can often have two people with the same family names who romanize it differently. But, continuing my point from above, whether you like the system they used to romanize their name (that is, if they were aware of a particular system at the time) or not, you should continue to romanize it the way they do.
Otherwise it would be like me always spelling someone’s name “Geoffery,” because I think that is the “more appropriate” spelling, rather than the way they actually spell it… let’s say “Jeffery.”
If it is the accepted/official spelling, whether you like it or not, use it.
Just my NT$2. Besides, I hate using romanization of all types, even the international standard Hanyu. I think they all can be utterly confusing. Why is the first sound in the word for “meal” (i.e., I’ll have meal #1) romanized as a “c” in Hanyu? “ts” would make more sense as it is closer to the sound? “tsan” rather than “can.” I always want to pronounce it “kan” when I see it. And, anyway, most Taiwanese don’t know it, so good luck finding out how to pronounce a new character/word from your friendly neighborhood Taiwanese using pinyin. I’d rather use bo-po-mo-fo. But, I digress… as I know romanization is needed for the non-Chinese speaking/reading public.