Well, what you could try is an engine that's designed to crawl specific niches and then allowing people to run their own instances. So you don't run any hardware yourself. You just let other people provide it - they might find a way to make money from it, or their community might find ways to pay for it anyway. It's not necessarily true that every search engine has to search the entire web.
The problem with this is that you get significant benefits from a larger crawling corpus, even if you index just a small portion of it, the rest will inform that portion.
That's a real problem that is ultimately hard to get around. Like my index is fairly small as it is, but even so it requires more hardware than say a student could afford. Like it's not enough that I'm dependent on external funding, but it's still not something you slap together for fun and then get bored of.
