Having received many t shirts from companies and conferences, I mostly don't wear them if the branding is really over the top. As described, a Kagi shirt would be something I'd actually wear
There was a hilarious blog post on here a few months ago from some guy who collects database company T shirts. A lot of them are quite bad but a few are really good. IIRC his favorite was from Snowflake.
I think I might still like the Snowflake one (3) the best though. Although rereading the article he says there is writing on the back of the Snowflake one which makes me not like it as much. There are very few stylish shirts I enjoy that have writing on the back of them.
For reference, that "some guy" is Andy Pavlo, a professor of databases at Carnegie Mellon. He has a lot of neat writeups online, like this annual review of new database systems [0]. He puts up lectures on the internet for free too.
Having been to Dr. Pavlo's office - or at least, one of them - I can attest to there being multiple cardboard boxes filled with gifted shirts from different companies. One of my favorite designs was actually from CMU's DB group itself - it has a little "this database kills fascists" tag on it, with a skull motif :D
But isn't the goal of the t-shirt a gift for the first 20k paying users? The goal for them doesn't seem to be about what they get back from giving away the t-shirt.
Based on their public data, they have 20,000+ paying users, and 1500 users paying for the family plan, which if all of the users are on the cheapest $5/month plan (which, many probably are on the $10/month plan like myself, as that gives you unlimited searches) would give them $100K+ each month.
Sounds pretty sustainable already to me, unless they have a really large team and/or really inefficient infrastructure, neither which seem true to me.
The expensive parts of the infrastructure are not their own, and the expense will scale by number of requests.
Back of the envelope:
The Bing API costs about $0.015 per query at the most cost effective tier. Kagi's highest revenue per query pricing is $5/300 queries = $0.166 / query. That's pretty slim margins, and only made worse by the $10 tier.
Now, they can of course start doing exclusively their own crawling, indexing and ranking and avoid paying some larger search engine for API access. But for that to be cheaper, they need orders of magnitude more scale
Kagi has a bunch of different sources, it doesn't seem like all results come from the same source, so without any particular insight into how each query works behind the scenes, I'd gather it be very hard for any of us to come up with an average cost per query like you tried to do.
Edit: apparently his favorite was from mongo: https://www.cs.cmu.edu/~pavlo/blog/2016/07/my-favorite-datab... which I have to agree with, that is a good shirt.
I think I might still like the Snowflake one (3) the best though. Although rereading the article he says there is writing on the back of the Snowflake one which makes me not like it as much. There are very few stylish shirts I enjoy that have writing on the back of them.