Why the pinyin of 鱼 is yú instead of ǘ? Two observations：


It should be fine for the pinyin of a character to contain no initials such as 阿(ā)，哦(ò) and 噩(è).
The bopomofo equivalent is ㄩˊ, which is ǘ in pinyin.


Then why the pinyin of 鱼 is yú instead of ǘ?
Under the section Pronunciation of initials for the pinyin page on Wikipedia there is the following:


  
  Note on y and w
  
  
  Y and w are equivalent to the semivowel medials i, u, and ü (see below). They are spelled differently when there is no initial consonant in order to mark a new syllable: fanguan is fan-guan, while fangwan is fang-wan (and equivalent to *fang-uan). With this convention, an apostrophe only needs to be used to mark an initial a, e, or o: Xi'an (two syllables: [ɕi.an]) vs. xian (one syllable: [ɕi̯ɛn]). In addition, y and w are added to fully vocalic i, u, and ü when these occur without an initial consonant, so that they are written yi, wu, and yu. Some Mandarin speakers do pronounce a [j] or [w] sound at the beginning of such words—that is, yi [i] or [ji], wu [u] or [wu], yu [y] or [ɥy],—so this is an intuitive convention. See below for a few finals which are abbreviated after a consonant plus w/u or y/i medial: wen → C+un, wei → C+ui, weng → C+ong, and you → C+iu. 


Also under letters for the orthographic rules of pinyin it says:


  
  Syllables starting with i are written as y in place of i (e.g., *ian is written as yan). Standalone i is written as yi.   
  Syllables starting with ü are written as yu in place of ü (e.g., *üe is written as yue).