Drawing on Washington state law, there is a law (RCW 18.165.150) that "any person who performs the functions and duties of a private investigator in this state without being licensed" has committed a gross misdemeanor. A "private investigator" is defined in RCW 18.165.010 as "a person who is licensed under this chapter and is employed by a private investigator agency for the purpose of investigation, escort or body guard services, or property loss prevention activities", which is not particularly helpful since it suggests that you can escape punishment by not being licensed. Looking beyond the ham-fisted wording, the legislative intent is clearer when we look at the definition of "Private investigator agency" is defined in terms of the business of
detecting, discovering, or revealing one or more of the following:
(a) Crime, criminals, or related information;
(b) The identity, habits, conduct, business, occupation, honesty,
integrity, credibility, knowledge, trustworthiness, efficiency,
loyalty, activity, movement, whereabouts, affiliations, associations,
transactions, acts, reputation, or character of any person or thing;
(c) The location, disposition, or recovery of lost or stolen property;
(d) The cause or responsibility for fires, libels, losses, accidents,
or damage or injury to persons or to property;
(e) Evidence to be used before a court, board, officer, or
(f) Detecting the presence of electronic eavesdropping devices; or
(g) The truth or falsity of a statement or representation.
We can take this to be a characterization of what a private investigator does, thus doing these things with a license is a misdemeanor. In other words, unlicensed finding stuff out about a person is prohibited by law, if you do this professionally. The state has asserted the power to regulate and license businesses. Note that even the collection of Googled information about a person would be discovering or revealing facts about a person (more disturbingly, academic research could easily constitute discovering the habits, activity, movement, or whereabouts of a thing).
However, there is no statute that penalizes a person for hiring an unlicensed PI (or, hiring an unlicensed contractor, etc.).
As for why private investigators are regulated, the number of regulated professions is stunning. Geologist?! I'm not aware of the specific political events that gave rise to this regulation, but as usual it was probably because someone did something bad and the legislature decided to expand its regulatory power to quiet the public outcry. A valid consideration is that they are often armed; it is possible that there are special dispensations where government agencies have to keep certain information from the public, but may provide that information to the police "or licensed private investigator" (this is just conjecture); or, persons and businesses may adopt privacy policies with exceptions for "legitimate investigations". I can't find a list of special powers of PIs.
I don't know of any challenges to the breadth of the law, which one could categorize as unclarity. I've never heard of an academic researcher being prosecuted for investigating the nature of a thing, so there probably isn't much case law that points to the legality of that absurd interpretation.