Except the examples you've given like extroverts vs introverts are not scientifically rigorous and the terms already existed well before him all around the world in different cultures (outgoing vs shy/retiring etc).
Actually, if you could give me your definition of scientific rigour that would probably help.
I consider science to be the art of making correct predictions. So you need a hypothesis (in the form of equations or computer programs) that can be tested on observations leading to correct predictions.
Extroversion/introversion might be scientifically rigorours by that definition (they might have done quantitative studies) but I'm not sure Jung did those, and even that it makes sense to create such a classificaton - people are a lot more complex and I don't really see the need for use of such classifications.
That's a problem I see with psychology, sociology, economics, and other "soft" fields. The quantification of things which are far more complex than the simplistic models created to the point that they are essentially meaningless. It's meaningless to quantify people into races or skin colors and that's about the level that those sciences are at.
Multiple regression (OLS) had not yet been invented. I'm not sure how you expect Jung to have used an apparatus of statistics which really wasn't developed (till Fisher) into a coherent whole when Jung would have been in his forties, having already written a number of books.
Statistics in the sense of looking at populations did exist, but the whole apparatus of modern statistics was developed in the early part of the 20th century, concurrent with Jung.
I agree with your definition of science. Incidnetally, Hans Eysenck developed a physiological test for extraversion/ introversion in the 1950's involving the amount of stimulus required to become noticeable to a person. This has been comfirmed by further research.
Speaking as a (soon to be) psychology PhD (all going well...) I would argue that the "soft" sciences have the exact opposite problem, in that, jealous of all the cool theories of the physicists they have attempted to jump straight to the theory building without the benefits of hundreds of years of observation.
I agree that models in the soft sciences are somewhat simplistic, but I actually think that they're not simplistic enough. We (as a species) need to figure out some invariants if we're ever going to do successful science on people and the systems we create.
Back to Jung, while he didnt use the statistics that we would today, he did spend an awful lot of time attempting to figure out why we are the way we are, without resorting to sex sex sex (like the inimitable Freud). Personally, at this point he's probably better read as a philosopher and student of human nature, but he is well worth reading in that capacity.
That being said, he's an awful writer so it is a bit of struggle. Well worth it though, in my opinion.
Funnily enough, I agree with you on psychologists and psychiatrists (to a certain extent). We understand so little, and claim to know so much. Our sample sizes and cultural range is quite poor (anthropologists are good at this, but they tend to lack even a basic understanding of statistics). I do believe that algorithmic approaches to predicting humans have potential, and the reason I now work in the private sector is to get access to some of this data as I believe that masses of data are the only way we'll get invariants to form useful landmarks towards understanding of people.
I would note, however, that I suspect you are classing pychologists (or cognitive scientists, as some of the hip american departments have rebranded themselves) as therapists, which although a common misconception is about as accurate as saying that computer scientists are software engineers (i.e. sometimes, but its not a one to one relationship). Thanks for the discussion, I enjoyed it.