The value proposition is in surfacing a result that you wouldn't already have from the free search engine. Your personal calculus will of course vary but lets do a basic business case with the following assumptions

Free search engines work 95% of the time for your employees searches

Kagi can get a result in half of the remaining 5% (this is definetly the biggest assumption and I haven't had enough experience with kagi to say if this is realistic)

Your employee does 1 search a day and 30 days in a month (so kagi gets you 0.75 more completed searches a month).

It takes an employee 15 minutes to search manually through documentation or come up with a solved algorithm from first principals when the search fails.

In that situation your employees time needs to be worth less than $53.33 dollars an hour for the $10 dollar plan not to break even.

So play with the numbers how you want to make up your own mind but it does seem reasonable to argue there's a market for it at that price. Personal use where missing a result could have no cost is ofcourse another question.

edit: 0.75 not 1.5 searches a month extra