Great question Dave. One that I think has many answers.
As pointed out by others, back in the day there were so many cars fielded by an owner, and driven by a hired shoe. I'll have to go back and look at a program or AARN from the late 60's/early 70's and go look over a typical modified lineup an look at the percentage of cars had hired rides. A typical starting feature in the very early 70's would have Brenn Sr. #24, Norcia #81, Deasey #707, Bullock #76, George Taylor #93, Silliman #4, Schloeder #K46, McMann #4, Horton #43, Scarmadela #7 or #121, Fodor #13, Marks #1, Ferriaulo #73, the Hustak #71, and more... That's over 1/2 the modified feature starting field where the car was owned by one person, and driven by somebody else. (Wow have things changed....)
I'm thinking the main reason for teams to split would be that if a team had a run of bad finishes/wrecks.... the owner would probably be thinking the driver was the issue, just about the same time the driver was thinking that the car/equipment was the problem, and not long after, they'd go their separate ways.
I'm thinking that a lot of us probably had a gut feeling for who was moving up the ladder, and who was moving down (who was stepping into a better ride, and who was stepping down....)
It was also interesting to see what new pairings would work, and which ones just never really worked out. Stan in '70(?) & most of '71, behind the wheel of the Deasey #707 was magic.... Stan and Deasey parted in the later part of '71, and Stan went to the Brenn #24.... Stan in the Brenn #24 found even more success right away at the close of the '71 season, and then through all of '72, and for a good part of '73. Stan and Brenn Sr partied ways I think around August of '73... Stan won a big race before year's end in the Chesson #76. Stan started 1974 in the Norcia #81, and I really thought it was going to be the power team of the decade.... Stan and the Norcia team parted only a few weeks into the '74 season after a tumble all the way down Flemington's backstretch.
Thanks for putting the question out there Dave. Very interesting.