I suspect their core business is unsustainable as is. From what I understand, they use search APIs, which are expensive. So they need to get their own index, at least partial, to have a sustainable business.
Kagi employee here. The search business is sustainable, we don't need a push in AI things to make it work. We're looking at these features/ideas because we think they complement search well, not because we need them from a cashflow perspective :)
Duck Duck Go uses the Bing API and they've been around for a long while. I'd imagine there's a heavy 80/20 rule of data that needs to be indexed frequently that people also search for, so those same cached results from API calls get the most use.
I don't think it's a fair comparison. Every single other search engine sells ads including ddg. Sure, they don't track you, but will still serve ads for your quesries.
Kagi is explicitly an ad free subscription. Comparing profitability is not straightforward.