Ruapuna circuit near Christchurch NZ used to run open mixed practise sessions. I saw and reported the incident which stopped them.
Testing a bike, a couple of bikes out on circuit and a couple of cars - well spaced. The guy on my bike came up behind a saloon car going slowly.
Lined him up to pass on the side with the most room on the front straight. At that moment the car starts weaving from lock to lock - nearly knocked the bike off track.
Rider backed right off and came in as soon as he could get off track - very upset.He'd actually been hit by the car.
We went and laid a complaint with the track manager. Car driver spoken to and hauled up before the Car Club committee. Negligent in not looking around before weaving - and tossed off the track for a 3 year period. Don't think he came back.
Sessions are now 1/2 hour alternating bikes and cars. Any sidecars get a separate 1/2 hour.
Nearest we ever get to cars and bikes competing together is the annual Brooklands Trophy. 3 vehicle teams run as a relay - separately - but closest team to a specified time wins.
Cars are Historic club, bikes local Classic race club. Honours just about even I think over nearly 20 years. Usually run at a combined meeting at Levels track, Timaru.