It is true that modern funding of scientific research is flawed. Certainly in the US and probably everywhere. Almost any working scientist has plenty of stories about the silliness of bureaucratic requirements for governments, universities, or nonprofits. Almost any working scientist can name some people in their field who they think are severely overrated or even unethical (this seems to be more of an issue in lab sciences, somehow). Almost any working scientist has peer-review horror stories and admits that the process is noisy at best.
Still: there are real benefits to being a non-independent researcher. At this point it’s hard to get to the forefront of research — in pretty much any field — without extensive contact with the people who are there already, most of whom are not independent researchers. Failure to do so doesn’t just mean you want produce hip research that caters to the specific elite tastes of the establishment. It also drastically increases the likelihood that you’re wrong. Good research is hard; it’s even harder in isolation. Ther are hundreds and hundreds of papers about your favorite math/physics/computer science (it does seem easier to be an independent naturalist or something) conjectures floating around out there. Many of them sucked away years of their authors’ lives, and somewhere around 0% of then are correct.
I suppose my two cents for anybody seriously interested in independent research is to make it as easy as possible for credentialed researchers to interact with you. Learn what you can, read accepted literature, acquire some credentials yourself if possible, learn the language on Stackexchange or Mathoverflow. Definitely do not open your interactions with grandiose claims. Most researchers actually like their subjects; if you have something useful to tell them, they want to know. You just gotta make it as easy as possible for them to see you’re not a crank.