You definitely want your doctor, optometrist, dentist to be licensed. You definitely want your wiring to be done by a proper electrician. You want your new building signed of by a licensed Engineer. Etc.. General carpentry is a little bit different, but those with proper apprenticeships are considerably more likely to be better, but in that case, it's not a guarantee.
The wikipedia article you presented as evidence has some troubling issues. Much of it is focused on the fact that 'without licensing' there's 'more growth' in the given field of employment, which is obvious and mostly beside the point: the issue is competence. When measuring quality they mention "find that occupational licensing of dentists does not lead to improved measured dental outcomes of patients, but is associated with higher price" - which is deeply disingenuous because it's likely related to specific kinds of licensing as oppose do the 'material issue of competence' which is the fact said dentists actually attended dental school. Can you imagine for a second someone giving you fillings, scrips, pulling out teeth, x-rays without having gone to dentistry school?
What the state needs to do is make clear which occupations are licensed, which are not, and the kinds of work that can be done otherwise. Replacing a doorknob or a water faucet may be a bridge too far for licensing requirements, but doing anything 'load-bearing' for example might be within the purview of regulation.