Ramanujan (post #4) was around a century ago, same for Einstein (post #7).
Before about the mid 19th century a great deal of important science, if you go back a bit further, virtually all of it, was done by amateurs. Darwin was an amateur. Arguably, so were Newton and Galileo, because, even though they were professors, they were professors of mathematics, not of physics (then considered a branch of philosophy, a separate professorate) or astronomy.
However, since well before the time when the Nobel prizes were instituted, and ever increasingly, there has been very little place of the amateur in science (except in some very special cases, like discovery of comets and collection of natural history data). Part of this is a matter of access to specialized, very expensive equipment and the skills to use it, part of it is the need for access to (and immersion in) the specialist literature, which is the only way to truly know what the problems are that need solving, but a big part of it is simply a matter of getting your voice heard and considered. In science, it is not, and never has been, simply a matter of being right. It is a matter of being able to convince the scientific community that you are right, and, yes, a big part of that consists in having the right credentials, speaking the right language, and making the right references to the literature. Even then, it can be very difficult, and a long road, for even a well accredited scientist to get a fair hearing for a radical new idea. It is more difficult than it was back in the days of Galileo, Newton and even Darwin, because there are far more scientists around who need to be convinced. This is, however, as it should be, because most radical new ideas are indeed wrong, and the barriers that science erects to getting them heard (and thus wasting time and resources on them) are a large part of what makes science work as an institution and a system for sifting truth from nonsense.
This was true even in the 19th century. After Darwin conceived of his theories of evolution and natural selection he kept the ideas strictly to himself for about 20 years, during which he gathered evidence, honed his arguments, and built himself a good reputation as a sound, respectable natural historian (mainly through his detailed studies on barnacles). Other people (and not just A.R. Wallace) had insights similar to Darwin’s, but Darwin rightly gets the credit, not because he was the only person to have the idea, but because he was the one who did most of the work (both in gathering evidence and in writing, and making clear, elegant arguments) that led to the idea being taken seriously, and eventually to it sticking.
The OP imagines a scenario where a college dropout publishes a brilliant new insight into quantum gravity “directly to the public”. No, he would have no chance of getting a Nobel Prize, not because the relevant Nobel committee would be biased against him, but because there is (as things are now) no chance that the relevant scientific community would give any attention to his ideas, and decide they were correct. Being right is very far from enough in science. The important thing, and the much harder thing, is persuading enough of the right people that you are right. Even if, by some weird coincidence, a real scientist were to become aware of the amateur’s ideas, work on them, and eventually amass enough evidence and argument to persuade the relevant scientific community that they were right (it takes a lot more than a single paper), most of the credit would go to that scientist, and not the original amateur, AND RIGHTLY SO. Clever ideas and “insights” are ten a penny; evidence and arguments sufficient to persuade the scientific community that your insight is actually correct takes a lot of work, often pretty much a whole career. That is the sort of thing that wins Nobel prizes.