> but if one exists, it would be individual state law since corporations are incorporated at the state level.

Correct. My understanding is that every state has an equivalent law. I can't give any citations really, though - my own state (WA) buries the responsibilities and requirements for registered business' registered or agent addresses in multiple separate sections in the state law website.

Every state requires a registered agent with address within the state. But that is not the same thing as requiring a business to reply to correspondence.

Yeah, if that was the case you could snail mail DDoS them.

Not if only bona fide requests need a response. If it came before a judge, you'd need each of those requests to mention valid actions regarding valid accounts without absurd/abusive redundancy.

They'd have to open and read the bad requests to filter them out and find the good requests.

I imagine you could put up some "SnailFlare" DDoS protection service in front of your head office.

Uniform Commercial Code (UCC) is standardised across all US states, Washington, DC, and territories:

https://en.wikipedia.org/wiki/Uniform_Commercial_Code