Just a few thoughts on this...
#1 Google's results are already spoilt. As the OP pointed out, they are optimized to generate revenue and not to provide the best user experience or the most accurate/useful information. I believe the "offer just good enough results that you don't give up entirely" analysis is spot on.
#2 Therefore, I like the idea of not just handing the poisoned fruit on to Kagi users to deal with it individually, but to make a collective attempt to add an antidote. And since the bar is set pretty low, I suppose that even a flawed implementation would likely do more good than bad.
#3 I love the idea of collecting this information automatically, but my guess is it can't be done. For Google, linger time = user attention = money. From the user perspective, however, it's much more complicated - I may linger on a site because it has lots of information, or because I'm desperate and the information is hard to find. Just the same, downgrading a site because the visit was brief might punish a webmaster for giving me what I needed in an instant, instead of forcing me to read five paragraphs of bullshit that were written for bots. And then, there's odd users like myself opening half a dozen links in different tabs before even looking at them, which might throw off any kind of automated analysis completely.
#4 So for me it would probably be down to manual input. Most of the Net was written so it can be processed by bots, and imho that is why the results are so frustrating. To undo the mess, it would seem to me the only way is to process sites with human eyes and brains. And yes, I realize that is 100% against the current trend.
#5 So then it would boil down to making the feedback part as painless as possible. Come up with an extension that is customizable and will only take a few seconds to give feedback. And above all, figure out what kind of information is truely relevant: Thumbs up/down won't do here, and offering 20 options to choose from is going to be too much work, so participation would tank.
#6 Shooda's remark about the "tragedy of the commons" for Kagi search seems like a good benchmark, if the feedback collected twists the results in the direction of "common taste" or makes special interest information harder to find, then it was probably the wrong feedback to begin with. To me, along with commercialization, it's the biggest search issue these days, that results are tweaked towards what the majority likes: If 99% of users are looking to buy cars and 1% are looking to build them, then "buy car" is going to give you information on which car to buy, while "build car" is going to get you information on which build to buy (not yet, but you get the idea). As a result, the most valuable information on the Net has become impossible to find, simply based on algorithms measuring if the bulk of users is fine with the results. KAGI NEEDS TO STEER WAY CLEAR OF THIS.