No, a neat solution to one, not at all theoretical problem: how to maintain a append-only database (eg mapping domain names to registrant public keys and (less critically) append-only lists of signed IP addresses) without giving any participant the ability to either redact the database (eg remove the registration for thepiratebay.org) or prevent (specific or any) future appendments (eg, prevent new IP addresses for thepiratebay.org).
You're quite right that "solution in search of a problem" is not accurate, though.
Well you need protection against 51% attacks, which means you need it to be very expensive to get that many modes, which means the people running nodes need to be compensated for their expense.
Which can be done neatly by having the things in the database have value, so that the reward can also be inside the system, i.e. mining coins.
Other databases people come up with always have problems with 51% attacks, so the system isn't made completely open, so it's pointless because then more traditional solutions are better.
You're quite right that "solution in search of a problem" is not accurate, though.