I know of no regulatory requirement that requires a Soldier to be licensed on a piece of equipment to perform PMCS.
The licensed operator should be the individual starting the vehicle and operating it. The Soldiers who are not licensed should be taught proper PMCS procedures using the -10 and how to fill out the 2404 by the licensed operator. They could do Before and After operation checks as long as it did not require operation of the vehicle.
Most units have a maintenance class and licensing program that Soldiers must attend to ensure they are properly trained on PMCS and properly prepared to operate a vehicle.
I believe your concerns are valid as they present a safety issue. Any Soldier who has an accident and is not a licensed operator or properly trained in PMCS cannot usually be held liable for damage. In this case the leader supervising the operation and having knowledge that the Soldiers are not licensed/trained would most likely be held accountable. I encourage you to raise this issue with your chain of command and propose a potential solution such as: Ensure there is a licensed operator present (from another section in the unit) to assist the Soldiers while they perform PMCS until they are properly trained and licensed.