Sometime in the early 20th century, usage of the now-historical kana ゐ and ゑ (and their katakana equivalents) dropped off, being replaced with い and え in modern Japanese. What exactly happened here and why?
Because the pronunciation was lost. "Wi" and "we" are still in some dialects, but standard Japanese does not have those sounds. These characters were just spelling. Similarly in English, we pronounce "through" as "thru" because the "gh" sound is long gone and "thru" is now a common variant spelling used in the US (I.E. Drive Thru)
After World War II there was a massive language overhaul, and they changed/standardized spelling and also made the Toyo (revised to Joyo) kanji list.