I have ridden with many of this private "unlicensed taxis" and I have not seen a official Taxi driver license in anyone. You know the yellow one with a picture stating the drivers name. However I spoke to one time that could speak very good english, and after we talked a bit she even told me she didn't even have a Driving License and when I question about it she told me she knew a few other drivers also with out any driving license driving taxis. She say no problem as long as there is no accident, but if she caused an accident her premium insurance would not cover her car only the other one. When I asked her why not get a license she answered, "Why should I? If I ever get stopped the official fee is 200 Baht, and police probably ok with 100 Baht not have to do the paperwork.
So, based on only anecdotal information, then.
"I have ridden with many of this private "unlicensed taxis...".
What is a "private, unlicenced taxi"? Where are they operating and how do you manage to hail one of these "many" taxis? Are you referring to the likes of Grab, Bolt, etc.?