The board generally controls everything, including who the chairperson is. Founders should maintain board control as long as possible, hopefully until they leave voluntarily. They're the least likely people to destroy the company. They're the most qualified to run it (having created it) and the most incentivized not to destroy it (owning a large part of it).
I’m not convinced that they are always the most qualified to run it. I’ve seen plenty of good technologies founded by people who are terrible at executing.