How many is unlimited? Presumably they don't get unlimited searches for $10 and, inevitably, someone will use more than they planned for. How much more than they expected is considered "fair use" or however they want to term it and why can't I know that before I sign up instead of guess I'm within what they are thinking?
Whatever the cap is, I’m sure it’s a lot higher than google will let you do before they start rate limiting you or making you do a captcha for every search. Pretty much all search services have some cap, after which they will put up roadblocks to slow you down
When trying out Kagi (prior to unlimited searches) my monthly Google searches were significantly higher than the cap. While some definitely do get CAPTCHAs, I wasn't. Adjusting this to the new unlimited price and it would still seem to be negative profit for them, hence the question.
While I think your questions are definitely relevant, in practice, you search less than you think.
I consider myself as a heavy search engine user but, based on Kagi stats, I was surprised how much less I actually searched compared to my estimate. My actual range is about 500-800 queries a month when I originally estimated upwards 1500 queries a month.
I tried Kagi and ended up hitting limits. Unlimited sounds nice, especially since I don't need to worry about how I'm "running out of searchers" so to say, but only once I know how much it actually is instead of just assuming "well, most people don't search much".
For $10 their cost for someone constantly typing new searches is significantly negative. It's surprisingly expensive for them to do a search and doing 1 search every 30 seconds for 8 hours is ~3x more than the cap of their $5 tier. I'm not saying that's a reasonable usage case for me I'm just saying the limit on profitability occurs SIGNFICANTLY sooner than "as fast as you can type for a month".