I understand the intent of your proposed new rule and I do agree with the intent. An inexperienced driver can get someone hurt easily.
I think you first need a definition for what is a driver who isn't up to the task. Something much more specific than having 2 other drivers say this guy is no good. Once you have a stated criteria, then I think you must figure out a way to get this person the needed training.
For some, karting is their first entry into the world of motorsport. I don't think you should just deny them access. Instead, once they have been identified, they need to be nurtured some to get them on the right track.
Do stick with your idea, just work on the specifics a little.
Sometimes when you see an inexperienced driver doing something wrong, all it takes is about 2 minutes of telling them what they did wrong and what to do to fix it.
I hope this helps,