As a postdoctoral research fellow in artificial intelligence at a large university, and an open source "Gentleman Scientist" in physics and science education through the
open source science tricorder project in my evenings (I have two independent educational backgrounds), I think you've overstated the simplicity of things a great deal. I know you probably didn't mean it as such, but frankly the idea that I (as someone who spent 30 years in school to become an expert in my field) should only pursue research as a hobby after somehow becoming independently wealthy is absolutely ridiculous. It takes at least 10 years (4 years of undergrad, at least 5 years of one-on-one training in graduate school, and usually a 3-year postdoc) to take a bright high school graduate and train them to be a research scientist and the beginnings of an expert in a field. That's a huge amount of time and resources committed by a society in a highly competitive environment to some of its brightest individuals, and you're suggesting that afterwards they should simply pursue their research as a self-funded hobby because the society they live in has engaged in massive social program defunding (including education and scientific research, among other things) over the last decade in favor of tax cuts for the ultra-rich? Do you have any idea how much a decade of post-secondary education costs?
While it is true that some research can be done independently by one or two people with little equipment, and that historically some folks in those circumstances have made major advances (like the ones you mention), and other self-funded scientists will undoubtedly continue to in the future, this is exceptionally rare. Even significant progressive research building off the pieces of what came before it usually requires at least a small team of people, and a modest equipment budget. In the past the labs I've been in have had single pieces of fundamental equipment that cost as much as a small house. I do my research for the good of society, and generally for others to use. There is no way I could pursue my academic research on any independent budget that I will ever have. I spent most of my "extra" (non living-expenses) income from my academic job on open source research in my evenings as it is. It's not like $5k purchases a lot of research resources, it's an exceptionally tight and entirely self-funded budget.
You also bring up hackerspaces. I spend a good deal of time (when I'm not working on the open source tricorder project) helping teach folks how to design, make, and build at our local hackerspace. This is a fantastic resource for the community, and it's incredible to see people pick up new skills and walk out with something that they've put together over a day or a month, and every now and again a really interesting engineering start-up comes out of a hackerspace (like Makerbot). That being said, hackerspaces are primarily engineering centered and places for skill sharing making-related skills. I am unaware of a single case of any substantial piece of science coming out of a hackerspace in their entire history of existence -- but even if you could point to a dozen REALLY good papers that had come out of them, worldwide in the past decade, that's the same number of good papers that will come out of a medium-sized academic research institution in a day.
My mentor in grad school used to say that science is inherently a social discipline, and it took me a while to realize what he'd meant. Public research institutions like universities are filled with extremely bright and talented people who are (generally and largely) very good at churning out good and interesting research for exceptionally little cost compared to industry (Academic wages are generally half to a quarter of what they are in industry, it takes a month to write a grant that has any chance of being funded, and the equipment budgets are usually modest). The research in many cases is openly published and available for use, and is only moving more in the direction of open access. The issue here is that as a society we invest a great deal of resources into incredibly bright people who work for relatively little simply because they love what they do and believe in research for public benefit, and are massively defunding basic science research, and making the barrier for entry to (anecdotally, I'm still young) the worst levels the retiring professors can remember.