'm not sure there is even enough demand for paid third-party site search
With Google sunsetting their paid CSE, I think there is an opportunity. My company was using CSE. I switched to a paid
https://www.addsearch.com/ account. Believe it or not, some properties let their paid CSE go to free, which meant they were showing competitor ads in their site search.
Right now, you have a few alternatives
- free Google search... which will show competitor ads
- native search for the app you use... usually bad. Witness the search on The Core or pay attention to the size of your database on a Drupal site of any size.
- Apache Solr - works well and is the recommended solution for Drupal, but you really need some technical know-how and server foo to run this well.
I think a search engine could step in and offer what Add Search offers and make some money. I will say, I find Add Search very good and not that cheap really... $89/mo for 1,000 to 10,000 docs - I think that's a fair bit more than Google was charging for their paid CSE product.
It gives you fine-grained control of your index and how your search results present (like choosing a feature image and telling it which pages to rank for which term). There might be some conflicts of interest there with a search engine, but if they could apply your filters and knobs just to site search and not the general SERPS, I think it would be a product people would pay for. Add Search seems to be making it. Not sure if they operate in the red or the black. But something like Mojeek would have way more marketing muscle since they already have customers after a fashion.