That's the rub, isn't it? :)

It could create a market system for search terms, similar to NameCoin; it could allow "mining" by providing rewards for validated indexing. I could see there being huge incentives for a 51% attack, though.

Alas, I'm more of a UX guy than a crypto hacker, so such things are out of my ken. But I definitely see a market for a Distributed Autonomous Corporation that provides search, and it would have a much easier on-ramp with users compared to competing with DNS.

It can't, really. There's nothing remotely like web indexing in a crypto currency. Indexing websites is massively storage and bandwidth intensive, something which a distributed blockchain is not designed for. It's a nice idea to make a distributes search engine, but has nothing to do with Bitcoin.