@bolwic pinyin is literally a method to romanise chinese and is considered to be
the correct way to do so unless you're from the 1940s or smth.
also the example you gave WRT romanising 希 literally uses the wade-giles system which is considered to be outdated in basically every context that doesn't involve directly quoting old academic papers.
either way, as far as i can tell, shue isn't a valid romanisation of 雪 in any commonly used chinese romanisation method (I checked through wade-giles, yale, and some weird french one) since 'sh' usually denotes the consonant /ʂ/ rather than the consonant /ɕ/ that is actually used in the pronunciation.
either way, pinyin is by far the most commonly used method for the romanisation of chinese in the 21st century.
note: i'm not mad or anything i just happen to be extremely passionate about the chinese language so sorry for the word vomit lul