There is a reason that why and what are spelled with an <h>, and that’s it:
Pronunciation of English ⟨wh⟩ – Wikipedia
It is now most commonly pronounced /w/, the same as a plain initial ⟨w⟩, although some dialects, particularly those of Scotland, Ireland, and the Southern United States, retain the traditional pronunciation /hw/, generally realized as [ʍ], a voiceless “w” sound. The process by which the historical /hw/ has become /w/ in most modern varieties of English is called the wine–whine merger.
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The merger is essentially complete in England, Wales, the West Indies, South Africa, Australia, and in the speech of young speakers in New Zealand. The merger is not found, however, in Scotland, nor in most of Ireland (although the distinction is usually lost in Belfast and some other urban areas of Northern Ireland), nor in the speech of older speakers in New Zealand.
Most speakers in the United States and Canada have the merger. According to Labov, Ash, and Boberg (2006: 49), while there are regions of the U.S. (particularly in the Southeast) where speakers keeping the distinction are about as numerous as those having the merger, there are no regions where the preservation of the distinction is predominant (see map). Throughout the U.S. and Canada, about 83% of respondents in the survey had the merger completely, while about 17% preserved at least some trace of the distinction.
The merger seems to have been present in the south of England as early as the 13th century. It was unacceptable in educated speech, however, until the late 18th century. Nowadays there is not generally any stigma attached to either pronunciation. Some RP speakers may use /hw/ for ⟨wh⟩, a usage widely considered “correct, careful and beautiful”, but this is usually a conscious choice rather than a natural part of the speaker’s accent.
A portrayal of the regional retention of the distinct wh- sound is found in the speech of the character Frank Underwood, a South Carolina politician, in the American television series House of Cards. The show King of the Hill pokes fun at the issue through character Hank Hill’s use of the hypercorrected [hʍ] pronunciation. A similar gag can be found in several episodes of Family Guy, with Brian becoming annoyed by Stewie’s over-emphasis of the /hw/ sound in his pronunciation of “Cool hWhip” and “hWil hWheaton“.