frijole del alta There is in fact more than a couple of theories about it, though yeah you can bunch them all up in one big "4chan is a honeypot" theory.
It has existed for over a decade at this point, if not starting then at least popularizing back in 2008 when the FBI supposedly got involved according to m00t himself.
Some say the government runs it, some say that some of the mods are feds, some say the feds have access to the moderation tools and all of the databases in collaboration with the 4chan staff, and some say the feds fund it.
Going from the leaks, it's pretty unlikely any of it is true past the usual US government shenanigans and I believe confirmed government organization involvement by countries like Australia and New Zealand.
As far as I'm aware 4chan is "funded" by Hiro himself and one of formerly two sponsors which he bought 4chan from m00t with. The sponsors in question are the Smile Company (yes, that one Japanese toy-manufacturing company that gets featured constantly in the /a/ buyfag threads) and a KADOKAWA subsidiary company.
I'm fairly sure Hiro is rich too from being a Japanese celebrity.
