It's not the "greater fool" theory. It's more like language. A new word doesn't have to have a real connection to its meaning. The word "cat" isn't structured like a cat, and when spoken aloud doesn't sound like one either. But we still like to be able to refer to cats without pointing, so we agree on something inherently meaningless and tie to to that.

Fiat currency is the same way. Rather than point a giant network of contracts together in order to create some monster transaction that satisfies a few hundred people evenly, we just agree to respect the unique-but-valueless papers produced by the crazy guy who will imprison anybody who tries to produce those same papers. It didn't have to be these papers; it didn't have to be bitcoin. It just had to be something that had the necessary properties: unique, scarce, lightweight, secure, and, most importantly, used by as many other people as possible.