The governemnt cannot, as a matter of law, require us to patronize any particular private business. For the purposes of this thread, the government can only require listing by an "NRTL."
While, in prior times, "NRTL" was often a roundabout way of saying "UL," there are some important points to consider.
The first is that there ARE fields in which UL has a weak, or non-existent presence. Ever see a UL-listed car?
Then, there are fields in which UL has a secondary role; for example, the ASME boiler code, and ASME's methods, reign supreme in heating equipment.
Nor has UL been completely without competition. Factories' Mutual has always had a strong presence in fire protection matters.
All bets were off when, back in the '80's, UL decided to become an "ISO 9000" firm. To be fair, this move was consistent with UL's deliberate efforts to have as many of it's standards, as possible, be recognized as ASTM or ANSI standards.
In short, UL is a firm completely without soul, or responsibility for anything. "Their" standards are nearly always written by and approved by some other group. All UL does is 'administer' them as a private testing lab. In that regard, they are indistinguishable from a multitude of other firms.
UL, instead, markets it's trademark. They are by far the most recognizable, and sell themselves as the "Cadillac" of testing agencies.