Here is the most plausible explanation of who Satoshi is IMO: a team of people tasked by (most likely) a government agency with developing a crypto-currency as an experiment.
The project is over, the people involved in it are probably bound to secrecy because the work was classified. They cannot spend a satoshi of the original bitcoin because that would be theft, probably a felony, possibly treason, who knows - either way that bitcoin and all the keys belong to their employer, not them, so you will never see anything signed by "Satoshi" to prove who "he" is.
Here is the most plausible explanation of who Satoshi is IMO: a team of people tasked by (most likely) a government agency with developing a crypto-currency as an experiment.
I don't know why the hell the government would spend money and time on a project like this.
Pseudonymity for transactions, intelligence gathering, influencing... it's 'money' and 'network analysis' and both of those have a lot of uses.
Bitcoin is very well designed, so it's not unreasonable to think that a brilliant mind or a team is behind it. Governments employ lots of mathematicians, computer scientists, and cryptography experts who would possess the the skills and man-hours necessary to devote to such an endeavor; whereas a lone hobbyist would have had to get the design right the first time the scheme became public.
It's not even that much money to spend, relatively speaking. A state-level agency from any of the highest military spending countries [1] possesses well in excess of the computational power required to mine coins. In this case, they released it into to the community and now it's a fixture most use but never seriously question.
The UK's GCHQ invented RSA 4 years earlier than Rivest, Shamir, and Adleman [2], but this fact was classified for 24 years. I think this is a very plausible theory that explains why Satoshi has stayed silent, and why Bitcoin was invented in the first place: not for personal gain or pride, but national interests by a well-equipped state.
A nice way to transfer money to clandestine operations world-wide, risk-free, for example.
For example, to fund a spy in China, you'd need to pay him in Yuan but the Yuan is a highly controlled currency... and guess what e-currency is highly popular in China? Bitcoin.
Just transfer your spy a couple of btc and have him trade the btc for local currency, in an eyeblink. Prior to btc, e.g. the CIA and other spy agencies had to fly in (and hand over!) literal bags of cash.
Guess this is why the Chinese government tried to crack down on BTC so hard, aside from the fact that BTC allows bypassing their currency controls and an outflow of money.
Is there any evidence the CIA and other spy agencies don't still use bags of cash? There are some arbitrary things that spy agencies are pretty low-tech about.
> For example, to fund a spy in China, you'd need to pay him in Yuan but the Yuan is a highly controlled currency... and guess what e-currency is highly popular in China?
AliPay. Can any "e-currency" actually be described as "highly popular"? Sure Bitcoin is the most popular, but that doesn't mean that it's popular. Let's put it this way. My parents know what ApplePay is. They've never even heard of Bitcoin.
To add to the list -- another user already mentioned funding foreign clandestine organizations. The modern day equivalents of Iran-Contra -- another theory is a government or organization that wants to undermine central banking, or global reserve currencies.
Governments used numbers stations over shortwave for years for remote communication. It's not too far-fetched to see the utility of Bitcoin for a government entity. The only problem is that you still need BTC->local currency exchange to fund clandestine field work, and I'd bet there are several currencies you can't get via BTC.
If the work was classified and the people behind it were bound to secrecy, I would expect disclosure to be a one-shot affair: a big dump of documentation and code on WikiLeaks, say. That's not what happened. There was a paper, there was open source code, and Satoshi hanged around for years before disappearing. That would have been an insane level of exposure for somebody risking severe repercussions if caught leaking state secrets.
The project is over, the people involved in it are probably bound to secrecy because the work was classified. They cannot spend a satoshi of the original bitcoin because that would be theft, probably a felony, possibly treason, who knows - either way that bitcoin and all the keys belong to their employer, not them, so you will never see anything signed by "Satoshi" to prove who "he" is.