Thanks for looking into this, and for making the search engine in the first place!
If you think it's a bad default (I have no opinion here), you could always implement it as
kagi.com/autofocus. This would work for me at least for the use-case of a home-screen icon.
Or, this could be a setting that's set separately for Desktop and Mobile, so that @Value7609 could disable it on Desktop and I could enable it on Mobile.
It does seem like the other search engines do the opposite of what I want (the difference between mobile and desktop that @Value7609 observed is weird), but I don't think you need to be limit your features by what other search engines do (the defaults might be another story).
I'm not ready to make Kagi my default search engine because, for example, I'm still on 100 intro free searches. But I want it to be convenient when I do want to use it.
Of course, if you don't have the time and energy to work on this, I completely understand. Thanks again!