Iirc "waifu" just derives from a phonetic rendering of "wife" since many languages don't pronounce a single "I" the way English often does but instead always use "ai" or "ei" for that sound.
Apart from the fact that Japanese of course normally doesn't use the Latin alphabet, it's fair to say that a single "I" isn't pronounced like in English in any language that does. Basically every other language has the "i" either like the first vowel in "eternity" for the short or as in "steep" for the long vowel.
But yeah, phonetic renderings are very common in Japan, also with adjustments to make foreign sounds match the Japanese language logic. If you want to have some fun with it, try
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In the end, "waifu" definitely derives from the modern "wife", not the old spelling (which would have been pronounced basically the same as the modern "wife", give the letters "waif" to any speaker of a non English Germanic language, and they would pronounce it more or less like that).