I think this approach makes sense for services with a small number of users relative to the data they are searching. That just isn't a good fit for a lot of hosted services. Think how much that TB's of data would cost on Algolia or similar services.

You have to store the data somehow anyway, and you have to retrieve some of it to service a query. If egress costs too much you could always change later to put the browser code on a server. Also it would presumably be possible to quantify the trade-off between processing the data client side and on the server.