Email spam works exactly this way. I think what you are pointing out correctly, is that the percentage might be incorrect; the principle is not.
There’s nearly 8,000,000,000 humans, so there’s a ton of variety that one can’t even imagine, but probably none of them want to eat a bar of soap for breakfast each day even if you think there must be some rare 1 in 1,000,000 out there.
Putting 1 in BIG NUMBER is just a way we abstract away hard and intimidating questions.
Perhaps. But at least that's just on paper. Resorting to advertising means actually forgetting your visitors are people.
Spam’s success rate would be dictated by the percentage of the people who want the product in the general population after passing through the spam delivery funnel.
With the donations it’s completely different mechanism.
Nevertheless, the fallacy is that small looking number of market share is the smallest possible market share.
IMHO that is a fallacy. Although %0.01 looks like a really small number there's no reason for it for not being %0.001 or %0.000001. When people do napkin math , it's a common theme to say that "If we only capture %1 of the market we would be $$$rich$$$" and they proceed to find out that there are smaller percentiles than %1.
To receive donations people need to be sympathetic to you or your cause. You need to actively sell it, making it a considerable part of the user experience.
It's really hard to build that relationship with just one visit. Maybe there are visitors deeply invested in the situation and they may actually obsess with your product but you need to look into the analytics to see if it's the case. If there are visitors that appear to be visiting extremely frequently, you need to explore ways to ask for the money and for that you will need data(profiles of the visitors) to develop your message however the OP doesn't do detailed analytics and profiling. It could be possible to monetise it and even catch a few whales but chances are that you can also alienate those people with the wrong messaging, so you probably will need to do personalisation which requires data and cookies and what not, which means data collection and sharing permission popups.
Of course you can try your chances and pick a group of people that you believe are using your product and proceed with A/B testing etc instead of profiling. If you happen to choose the privacy nerds as a target you will find out how much the privacy nerds like donating.