There are several romanizations of Chinese. But all of them are just that, romanization of Chinese. They do not represent Chinese language. What they do represent is the pronunciation for a variety of Chinese. For example, describing Hakka as one language is inaccurate. It is best described as one major branch/variety of Chinese, with mutually intelligible and unintelligible regional dialects (or if you prefer, regiolects or topolects) of Hakka. Hanyu Pinyin is the romanization of Standard Chinese, which is based on the Beijing dialect and Dream of the Red Chamber.
The People's Republic of China uses Hanyu Pinyin as the only romanization of Standard Chinese pronunciation, unless it's Hong Kong. Hong Kong is a special case and uses Jyutping to romanize its own variety of Chinese, Hong Kong Cantonese, which, in formal form, can appear virtually identical to Standard Chinese (having Cantonese pronunciations) while in colloquial form, the differences appear more dramatically. The Republic of China uses Mandarin Phonetic Symbols, which is not a romanization at all.
Personally, I think if you want to indicate the pronunciation exactly, then the best method is IPA transcription, for the following reasons:
IPA is the International Phonetic Alphabet. It is the international standard.
Romanizations fossilize a very specific variety of Chinese, typically the prestige variety. Most Chinese topolects are not romanized.
Chinese people themselves may not be aware of these romanizations, aside from Hanyu Pinyin and Jyutping. So, using Wade-Giles or Pe̍h-ōe-jī romanizations would only serve to help foreigners or non-Chinese people.
Regional dialects are held to be without written form. This opinion is not special to Taiwan. In my own family, we speak a dialect of Southwestern Mandarin. My father, a native speaker in his dialect, will assert that regional spoken words have no written counterpart. Let speech be speech; let writing be writing. Therefore, the proper way to record and preserve speech is to use audio recordings and IPA transcriptions.
Most native Southern Min speakers in Taiwan are unfamiliar with POJ or any other writing system, commonly asserting that "Taiwanese has no writing", or, if they are made aware of POJ, considering romanization as the "low" form of writing, in contrast with the "high" form (Chinese characters).