I would argue that they cannot effectively go elsewhere and competing services cannot emerge. The reason for this is that the Google Search index has been built

I would argue that they cannot effectively go elsewhere and competing services cannot emerge. The reason for this is that the Google Search index has been built over decades into a unfathomable search index that is beyond compare. If the index were made public, with a usable API, then other companies could provide alternative search experiences, however developing an on-par search index is nearly impossible, even with the strongest venture backing imaginable. Furthermore, since google controls the index to the worlds information they are able to delist topics or pages that users may want to see.