I mean, presumably at some level you are using the search API - it's just a programmatic interface into the same underlying database calls. I don't know if Kagi web search uses the public API directly or if they share an underlying internal API, but I imagine there's not a lot of difference on Kagi's end.

The big difference is that API usage can be scaled up way quicker than web page hits and scraping can be, which is an understandable concern if you're trying to price your service for human usage and not for bots hammering away as fast as they can. But judicious use of rate limits could help here - have a subscribers API tier that allows only a relatively low volume of calls and do standard API pricing for all requests beyond that.

That said, I'm sure there are complexities here that I'm missing that make this easier to say than to do.