The points championship is for drivers, not car owners. I see no reason to change it.
A record from the dark ages of 1963 stands today and I'd wager will not likely ever be broken regarding drivers and owners involved in the hunt for the points crown.
Joe Weatherly won the championship in 1962 and somehow still managed to find himself without a full time ride for 1963. So he went looking for any seat an owner would let have.
Bud Moore offered "Little Joe" a ride for the major events and Weatherly drove Bud's car 34 times that season. For the rest of the races he hitched a ride wherever he could, sometimes in less than stellar equipment.
Little Joe managed to capture the crown that season in the final race at Riverside. Along the way he drove for a total of nine car owners.One of the teams he drove for was Petty Enterprises, the driver he beat for the championship; Richard Petty.
Never before or since had a driver won the championship driving so many different cars in the season. Odds are they never will.