What's the problem? Well, doing real scientific research is hard and time-consuming. Just trying to catch up with what's already known in your field of choice takes a lot of time and effort, especially if you're unplugged from the community, and then taking it to the next level by actually discovering something new is far harder. The average PhD student works for several years, full time, before they do their first piece of truly worthwhile work, and in 99 percent of cases we're still not talking about anything significant enough to satisfy your average hobbyist with dreams of scientific glory. Also the average PhD student has access to a zillion things which a hobbyist doesn't, most importantly an advisor who understands the field and knows what approaches are likely to be worthwhile. So for a hobbyist-scientist, we're talking four to five years of all your spare time spent trying to produce one or two papers that probably won't make a big impact. Doesn't sound enticing.
Crackpots, of course, get to take a short cut. Crackpots get the thrill of being a Great Scientist Who Discovered Something Important without the tedious mess involved with actually learning the field and doing science. Crackpots occur when you take the desire for scientific glory and subtract scientific understanding and self-awareness. They're inevitably extremely satisfied with their work, even if they're angry that nobody will take them seriously.
In short, though, anyone with the brains, the commitment and the love of science that you'd need to be a legitimate part-time citizen-scientist in this day and age has probably already found a way to be a full-time scientist instead.
What if you don't see any interesting results in your research? That's an inherent risk of research. People giving you money should be aware of that.
What if you don't produce anything tangible to give away? Depending on your goals, that's a real possibility. People giving you money should be aware of that.
What if people don't want to give you money? People giving you money should be aware of... well, okay, that doesn't make sense. If you managed to convince people to give you money, then we're okay on that point.
An example: what tangible benefit do people get out of donating to universities? A tax write-off? I guess, but is that really the reason why people donate? What about to the Salvation Army? Or to whatever non-profit org? People donate because they want to help and support the mission. I don't see why it couldn't be the same with scientific research.