I think Taiwanese (>90%) use Tongyong Pinyin for their (sic: English) naming.
There are some brave soul using Wade-Giles (sans the diacritics).
But I never know (notice) any Taiwanese using Hanyu Pinyin.
Changing a latinized translation system would means "correcting" all other people names. Learning from history, this usually didn't end well.
How'd you feel when reading/seeing: Taibei instead of Taipei, or Xinzhu instead of Hsinchu and Gaoxiong instead of Kaohsiung?
There will always be an issue of Latinizing language that is not written (originally) in Latin alphabets.
Japan and China sort it out (kinda).
Others, African countries, Arabic countries, India, Myanmar, Thailand, Taiwan and Korea unfortunately not yet.
On a side note: Do you think Americans would be agreeing of using British-spelling (i.e. correcting them "wrong" spelling of armor, labor and harbor?).
Think the issue like British English and American English, Dutch and Afrikaans, Spanish and South American Spanish or Portuguese and Brazilian Portuguese