We do have a feedback loop: this forum 🙂
We have served many reports of search quality feedback over our time in public beta. The problem with a low effort "report" button, is that in almost every case we needed to ask the user questions to find out exactly what they were looking for. If we had guessed, it probably would of been wrong - everyone has a different perspective and expectation, and sometimes it takes some discussion to get to the bottom of it.
If users just sent us "downvotes" instead, it would not be helpful. Kagi's quality would be much less than it is today, and it would be an even harder product to sell. We could add a text field, or a drop-down of misc. descriptors ("Spam results", "Irrelevant to my keywords"), but this is only a piece of the information we need, if they even fill it out.
Those who do end up taking the time to open a report often leads very high quality discussions of important issues (they felt moved enough to open a report, it must be important...)
The idea of course is a good one - but in our experience the it feels like the best bet is to instead make steps to optimize opening this line of dialog, such as somehow linking your account here (automatically creating one?) and automatically fill out a template post.