What Regulatory Requirements are Really Necessary for Sale in the USA?
To answer your question vaguely: no, there is no one set of golden rules which the U.S. follows as a whole when it comes to electrical matters.

It's the National Electrical Code which makes mention of 'listed' or 'labelled' devices, which is where the NRTLs come into play (UL, CSA, etc.). OSHA approves the NRTLs. The requirements will vary a bit from state to state depending on which code (if any) has been adopted.

Here's a map of the USA showing which states have adopted which versions of the NEC:



There are a few states which haven't adopted any version of the NEC, but have local jurisdictions (counties or cities) which have either adopted the NEC or some 'equivalent' laws.

That being said, I don't agree with your bashing of safety certifications. I personally will never plug an unlisted device into any outlet in my home. I've disassembled some of these 'cheap' gadgets with only China Export marks (meant to look like the European CE mark) or with counterfeit UL marks, and am stunned by just how unsafe these things can be. No creepage/clearance, insufficient wire gauge, damaged wire insulation, improper/no earthing, unconnected earth wires, inadequate fuses, the list goes on and on.