But for the most part the system seems to be set up so that you first spend a long time working for someone else and research their ideas, after which you can lead your own group, but then most of your time will be spent on applying for grants and other administrative trivia rather than actually researching the interesting stuff. Also, in Finland at least, all professors need to also spend time doing teaching, so that's another time sink.

This depends on the field, university, and maybe country. In many cases, doing your own research is the main focus from graduate school on. At research universities in the US, at least, doing research is a professor's main job - although they do also have to do some teaching, apply for grants, and so on, professors are primarily judged by their publication record. In graduate school, many students get to work on their own research projects. A common model is: a professor who has some areas of interest & expertise gets graduate students who are interested in doing research in those areas. At first the students might work primarily on the professor's projects, especially if they don't have research ideas of their own yet, but during their time at grad school a student is expected to develop their own research ideas (within the same general area) and do their own projects, with guidance from the professor so that they can learn to do it well.

I think the academic route should work pretty well if you're interested in topics that are an established part of an academic field. If you're interested in an unusual topic that is not so well established, then you need to look and see if you'll be able to make academia work. Will you be able to get articles about that topic published in academic journals? Can you find a grad school, and then a university job, where they will support & encourage your research on that topic?

If you can find any published articles related to the topic then that's a starting point. Then I'd make a list of every researcher in the field who is interested in the topic, starting with the authors of published articles. Then look into all the grad students who have worked with those researchers, follow citation paths, and so on. You can get a decent sense of what academia might be like for you based on publicly available info (those researchers' websites, their lists of publications, and so on), and then you can contact them for more info. If you do go to grad school, you might go to one of their universities, or to a university that they recommended.