Coolidge never really chose Hoover as his successor. After Coolidge announced over a year before the 1928 election that he would not be running for another term, he essentially kept hands off the GOP nomination process, while Hoover worked at getting that nomination. Coolidge made it clear that he supported Hoover during his campaign vs. Democrat Al Smith, but his role was small. During his last year in office, as he sensed that Hoover would succeed him, Coolidge fretted privately that a Hoover administration would lead to bigger government, deficit spending, and an economic downturn, reversing the achievements of Coolidge's administration. In that, Coolidge was absolutely right.
Treasury Secretary Andrew Mellon would’ve been a better successor to Coolidge, although ultimately I wish Coolidge could’ve served one last term.