They won't. Notice that Angies list doesn't operate on the "customer pays for the list" model. That's because any directory service that depends on the searcher paying suffers from the problem that once you've found what you're looking for, you have no reason to keep paying for the directory. If I need a lawn guy, I only need to find one, and then I have their number. Why am I going to keep paying the "Lawn Guy Directory" $5 a month after I found someone?

And if you're going to charge on a per-query basis, I note that Kagi isn't nearly as well funded or well known as Google, and that's with them offering an "unlimited" tier. And a per-query model disincentivizes me from using the service in the first place. The more digging I do, the more it costs me, so the more likely I am to take the first result I get back.

Even the most classic "direct to the people who are most interested" advertising model where the consumer pays money for the ads (magazine ads) still is almost entirely subsidized by the advertisers, not the consumer.