I've found that if people want to learn, then they will learn. You don't need a PhD for that, and the process of going through a PhD doesn't really teach you anything more than you couldn’t have gotten yourself. Passion drives someone to learn, not getting accepted into a PhD program.
They exist, but they're uncommon, and many of the people doing that kind of work are in sort of para-academic jobs, like long-time librarian at a big research library, or senior staff member at a (government or corporate) research lab. Even in an environment like Google, the majority of the papers and paper-like writeups seem to come from either people with PhDs, or people with long track records in a quasi-academic environment, like Google's sizable stable of ex-Bell-Labs researchers.
I don't really say that out of any particular love for institutionally tied research, but more out of the opposite, a frustration that it's so rare to find DIY research that really contributes to a research field. Some of that, I assume, is just incentives: if what you earn money on involves getting something to work, all that really matters is that you come up with a technique that works. Understanding how your technique relates to existing techniques, explaining whether it's completely novel or a variant of an established one, and doing the detailed analysis to figure out why precisely it outperforms existing techniques (e.g. is there one particular tweak that's critical, and if so, why is it critical?), is not always something incentivized in that context, but is important to advancing the state of knowledge in a field.
“In theory I agree, but I very rarely run into people who actually do so on their own” This board is full of people who actually learn on their own:) People learned to code, people learned how to run businesses and people have learned how to build purely based on their passion to learn/build and contribute to the world. The reason why this is less so in science is that the resources are behind a paywall. I recently left my academic life to start a business and as such, I don’t have access to scientific papers anymore….this limits my ability. This is also the major motivation for my startup which will bring raw academic scientific data to the public…but I digress. The fact is that you are surrounded by those people, but they aren’t bringing their ideas to science because the process by which science is done doesn’t allow for it…and that is a problem.
Re: peer-review papers/quality: ahha, I’m not sure I agree. Peer review in theory is great, in practice it’s BS/politics/$$$$. Also, in my experience (YMMV), a lot of references in intros/discussions are “oh shit, you have to reference Joe Schmoe’s 2008 paper here because he is on the editorial board.” Not to discredit your point, I agree that peer review papers, citations and the like are important, but they are being abused now (at least in bio).
This is long winded, but my point is that we don’t see a lot of people contributing to science because they don’t have the resources to do so. I think that needs to change soon and I’m working to make that happen.
Of course, the open courses being put out for CS and Math is certainly is changing the picture for these fields. I think they are great.
The point is, learning in a bubble is not nearly as useful as learning from peers and those more experienced as yourself. It's also the case that few people have the discipline to go through the important but sometimes dreary exercises required to learn these topics. Having structured learning programs helps with this too.