The biggest problem with this is figuring out when to switch. If you switch within a single example, you will confuse many readers. If you have a series of related examples, people will disagree about when it is reasonable to substitute a new person.
Using specific personal names (Alice and Bob are traditional) for each character can help with that, but it is still a problem. And using personal names brings up an cultural issues more directly than "Strunk and White" would. (If Bob and Alice seem neutral to you, would you do a double-take on Kehinde or Oladotun?)