Disney wrote in 1948's "What Mickey Means To Me," per The Walt Disney Family Museum, that the character came to him "at a time when the business fortunes of my brother Roy and myself were at [their] lowest ebb." The company was very, very far from the media juggernaut it is today (the humble business had only been founded in October 1923, per History, when it was known as Disney Brothers Cartoon Studio), and so Walt had both the availability and simply the need to provide his voice-acting talents.
Skyway To Wonderland reports that, increasingly, Walt Disney did not have the time to voice Mickey (and, at the beginning, Minnie, a role he also held until 1930). Apparently, substitutes like Clarence Nash (the original voice of Donald Duck) would perform the role when Disney himself was away on business or otherwise unavailable.
Behind The Voice Actors states that James McDonald became Mickey's regular voice actor in the 1950s, 1977 marked Wayne Allwine's first time in the role, and that Bret Iwan has starred as Mickey since Allwine's death in 2009. It also suggests another factor in Disney's decision to step away from voice work: his smoking seems to have given his voice a harsher, hoarse quality, hardly conducive to playing the adorably high-pitched mouse.
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