Citizen science can definitely be a thing, but it's going to have very different comparative advantages than anything based around established institutions, i.e. universities/research labs. It might well be that both of these are worthwhile problems to solve - they need not be exclusive.
Agreed, but I really object to the term "citizen science". It simultaneously implies that academic professionals aren't citizens and that the political question of citizenship (as opposed to, say, statelessness or nationality in a monarchy) is a necessary prerequisite to doing amateur science, or at least for doing it well.
I think it's likely that improving the options for non-institutional researchers will improve the situation for institutional researchers as well, among other things because it improves their BATNA in negotiations with institutional forces.
I'm not endorsing the term, but it's the established term of art for what you're talking about. "Amateur science" in particular has its own implications of shoddy, low-quality work, so that's out too. And "Gentleman scientist", which is the most historically accurate in many ways, is just too classist and sexist for modern sensibilities!
The "Amateur Scientist" column in Scientific American wasn't about shoddy, low-quality work (though it often was about making do with substandard apparatus), and neither is Bill Beaty's wonderful http://amasci.com/, nor are "radio amateurs" known for shoddy, low-quality work, so I think that term might be salvageable. Beaty's site suggests "science hobbyist" as well.
Probably none of "amateur scientist", "science hobbyist", or "citizen scientist" is good enough to serve as a reasonable reputational BATNA for professors considering leaving a university. "Independent researcher", maybe?
In the research literature I very rarely see references to "scientists"; that's mostly confined to the vulgar press. Instead it talks about "researchers", "workers", "investigators", or "authors", or until recently "philosophers". So from a shibboleth perspective "citizen scientist" is pretty bad; if you say "I'm a citizen scientist" you're implicitly contradicting your claim of membership by using the exonym.
The real BATNA for professors at a university is a job in the private sector, where PhD's and professorships are a valuable credential and 'independent' publication as part of research reports, etc. might still be possible. More independent research is all well and good, but it would not alter that arrangement significantly.
That's what the BATNA is right now, but it's disastrous from the perspective of public welfare because it requires you to dedicate most of your mental energy to the job.
