Pizza delivery chains are largely operated as franchises, from what I remember. Buying Papa John's would get you the existing relationships with franchisees and the right to use the trademark. It wouldn't get you direct access to drivers - their paychecks are paid by entities like Rain City Pizza LLC.

You can structure franchise agreements in a way that gives you control.

There's some evidence pizza chains do that. http://www.bluemaumau.org/15086/jury_smacks_domino’s_death_s...

Or they could just give franchise owners enough incentive to participate.