VPOTUS = White House Chief of Staff

What would happen if instead of creating a new office as his chief of staff, Ike gave the job to Nixon? Kennedy and Johnson didn't really use chief of staffs, but Nixon later revives the practice of giving his VP the Chief of Staff position, and every president from then on does it too. How does this affect history? In particular, does Ford still become Nixon's VP when the job is actually something of worth? What happens to the careers of Cheney and Rumsfeld, who were Ford's CoS?
 
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