You've asked if "the notion of privatizing" is good or bad, and I will respond unequivocally that it would be a good thing in general. (If we have licensing at all, that is, which is how your question could have started. You're starting with an assumption that licensing is perhaps necessary; I won't even stipulate that. Do driver licenses keep bad drivers off the road? Do hunting and fishing licenses keep people from poaching?)

On the other hand, will there be problems? That's a separate question, and the answer to that question - on nearly any basis that you want to ask any question about human endeavor - is that there will certainly be problems. The human condition is basically lurching from one problem to another, and resolving some along the way in some way that 'works' ... for various definitions of "resolved" and "works".

As you pointed out above, there are pros and cons to be considered on that issue.