The search front companies would use the index to retrieve pages, then they would rank these pages with their own criteria and filter with their own white/black lists, then present the result in their own UI. Each one would have their own ads and tracking (or lack thereof). The index would not be able to know the identities of the users.
In the end they all boil down to an "attention economy", it's about us and our eyeballs, we should have more say on what we are consuming.
The part about ranking, filtering, tracking and UI is true for FaceBook and Twitter as well, even though they are a different kind of service. We could have alternative views on these systems, where we have more control on the way the system manipulates the information for us.
In the end, the point would be to make Google closer to what it was at the beginning -- just input and output. No ads on top of it, no bundling with other offerings etc. And if the publisher's ranking remains as good as it should, then surely some will be willing to pay not only for the raw data, but the ranking as well.