My approach to answering this would entail:
1) Determining what percentage of search engine use is driven by the need for a short cut to information you know exists but dont feel like accessing the hard way
2) Information you are actually seeking.
My initial reaction is that making search engines irrelevant is a stretch. Here is why:
Regarding #1, the vast majority of my search activity involves information I know how and where to find but seek the path of least resistance to access. I can type in "the smith, flat iron nyc" and know I will get the hours, cross street and phone number for the Smith restaurant. Why would I not do this instead of visiting the yelp website, searching for the Smith, set my location in NYC, filtering results etc. Maybe I am not being open minded enough but I don't see how this can be replaced short of reading my mind and injecting that information into it. There needs to be a system to type a request and retrieve the result you're looking for. Another example, when I am looking for someone on LinkedIn, I always google the person instead of utilizing LinkedIn's god awful search. Never fails me.
2. In the minority of cases I am looking for something, I have found that Google's results have gotten worse and worse over the years. It will still be my primary port of call and I think this is the workflow that has potential disruption. Other than an Index, I dont know what better alternatives you could offer.