The seeming all-encompasing language at the start of 600 notwithstanding, it is not required that EVERY sign be 'listed.'
Disregarding the red herring of a sign that has no electric power, field-installed outlines, etc., need not be listed (600.3). In practical terms, the AHJ has no role once the final is signed off, and thus no control over what gets plugged in to the sign receptacle. It's beyond the scope of his authority.
My point regarding only some signs being covered by code was not, however, directed at the NEC. There are plenty of other codes that can come into play, and the NEC is but one of them. Unless we wish to send the OP off to another forum, we need to recognize these other codes.
"Listing" is simply irrelevant with many signs. I care not what sticker is placed on the sign; if you don't hang the thing in accordance with sign codes, you have a violation ... and probably a sign in danger of falling. That's where a 'beer sign' differs from something you hang over the sidewalk. Even a sign that is nothing but a painted board needs to comply with these other codes - though listing is not required. Your lowly beer sign, even if neon and listed, is exempt from these sign codes.
To assert that failure to enforce the code is malfeasance on the part of the AHJ is an argument that might have some merit. Just as important is that we recognize that 'listing' does not relieve the AHJ of his responsibilities. There appears to be an attitude that all the inspector need do is look for the sticker. Some of the most immediately dangerous things I've seen were composed entirely of 'listed' parts, installed according to the listing limitations and installation instructions. Some even had a PE stamp on them (Kansas City Regency Hyatt, anyone?)
I disagree with this 'listing' fetish the code seems to have developed over the last few cycles. Good heavens, we are a CONSTRUCTION trade. We MAKE things. Not everything has to come out of a box, complete, from some factory.
Read the fine print and the disclaimers, and you'll make the uncomfortable discovery that the 'listing' firm promises NOTHING as to a specific item. The sticker is no guarantee that the item meets any standard, or that the standard has any relevance (or wisdom). All that UL sticker means is that, at some point, a sample of the product was evaluated, and that sample met their standard, on that particular day. All that sticker means is that UL got the check, and sends someone out there from time to time for another one.
I will disagree that insurance underwriters are "AHJ's" Insurance is simply a private business transaction - they are no more your AHJ than you are the AHJ when you buy your morning coffee. Insurance is a simple market force - unless we muddy the waters by requiring someone to buy it. Mandated insurance is neither a market force, nor good government- but that's another discussion.