Vito never moved Tom out. He had turned the family business over to Michael when Tom was pushed aside as consigliere. Vito even consoled Tom, telling him, "I never thought you were a bad consigliere, I thought Santino was a bad Don, rest in peace."
I disagree. Vito does console Tom, but only after saying "I advise Michael." This indicates to me that Vito was on board with Tom's demotion, and maybe even initiated it.
As to why, I believe that Vito, anticipating Sonny being his successor, groomed Tom to be overly conciliatory to balance Sonny's hot-headedness.
Michael, both cool-headed and ruthless, did not need a counter-veiling force like Tom. Also, Vito may not have anticipated how threatened his Family would become. Tom was not suited for such a death struggle, as was clear to Michael and Vito.