He's asking if it's illegal, not claiming that it is.

IANAL, but a reasonable guess tells me that while shutting down the service wouldn't be illegal, you would still be on the hook for the requested data. You don't pony up, the Feds would, at a minimum, charge you with obstruction of justice and consequences would follow.

NSLs come with gag orders, and it's possible that the government would view shutting down a service entirely as a violation of the duty not to disclose. It gets fuzzy here, because we're speculating on how a secret court will rule on a body of secret law while working hand in glove with the NSA.

I'm not a lawyer, but I would bet that can be classified as "destruction of evidence".