I've often wondered what would happen to the content in EN should the company go belly-up. The company's recent downsizing and financial issues have brought the question even more often to the fore of my mind.
I recognize that the desktop clients have local storage of content, and that typically means continued local access if the online component goes dark. But some applications terminate app functions when servers go offline permanently. Are you sure EN would not be one of those? There's always the possibility that the cause of the online component ending requires that the desktop apps be rendered useless, too. For instance, in the event of EN losing a patent suit or for another reason being ordered to cease all operations. In that case, a court would give users the time to get their content out, but should one miss the announcement... Evernote Apocalypse.
Never say never. The entire point of backups is to act as insurance against the unforeseen, unlikely, or previously thought impossible.