10-28's/10-29's are mostly done via the MDT today for both efficiency and to protect PII.
Some specialized units without access to MDT might use their cell phones or the local A-TAC or L-TAC channel.
You may hear the occasional plate being run on the SCC access channel, but alot of public safety agencies are getting away from putting PII info over the air.
Fun fact: The old Freq Charlie (Car to Car) 39.480 is still being used by LA County Sheriff. It's used as part of the LA County Emergency Alert System. Most TV / Radio stations have EAS receivers that listen to it. The only real time you'll ever hear activity is the last Tuesday of the month when they conduct the monthly test.
SCC will still run subjects on the station's dispatch channels if requested to by a field unit. But most of that is done over the MDC. The only time I would run subjects over the air was if I was away from the car and didn't want to or couldn't wait for a reply. Also I would have new trainees do it a couple times, so they were familiar with the procedure.
I was a trainee when the MDCS was new and I rarely had a 10-38, but was forever reviewing hits and near-misses.
Based on radio traffic now it seems many more are run on the air and I don't hear SCC asking about returns much.