Google CEO Sundar Pichai seemed genuinely alarmed at the prospect of being forced to license Google’s search index and algorithm
This is almost exactly what Kagi suggested.
The hardest part of internet search is building the search Index. It's massive. Practically a whole copy of the internet. Selling other provider access to Google's search index means new businesses and new business models can be created. My only concern is the "and algorithm" part. That almost sounds like the current state of things. Where companies can run queries to google and receive standard results filtered by Google's algorithm. Direct access to the index is needed without Google's algorithm, so others can use their own algorithm. But maybe they meant and/or, so companies can choose to be a real "Google white label" or something more.