I'd hesitate to say almost every graphic designer has taken the career path you indicate. Most start out with some artistic sense and then build upon it.
There is an important distinction between "artistic skill" or sense and "drawing" which your linked question refers to. Every successful designer must have an artistic skill or sense. One must understand lighting, space, color, relation, proximity, balance, etc. All of these are artistic skills even if they do not relate to drawing specifically.
There are several careers which all require an artistic sense - Photography, design, architecture, writing, painting, engineering, etc. Pretty much anything creative requires some idea of what does and does not work with human perception. Then, depending upon the specific field, there are technical considerations to learn.
From the point of an artist looking to "commercialize" their talents it becomes a matter of learning the route of production for whatever field they are trying to enter. For example, if one wants to go into furniture design, all the best sketches and drawings in the world are no good if the furniture can't actually be constructed. The artist needs to learn about construction or physical restrictions then draw with those in mind.
This same aspect holds true for design. Having a great drawing ability can be very helpful. However, to be a designer you need to know about production methods for any specific area.
If looking at web design, a good designer needs to understand what is and is not possible with web building. I've always stated that a "web designer" who can not code by hand, is not a web designer. I don't mean complex .net or php applications, but basic front end HTML, CSS, and perhaps jQuery should be a requirement for any person referring to themselves as a "web designer". Just my opinion.
If considering print design one must learn about the entire print processes (platemaking, imagesetters, stripping, separations, etc) in order to be a great print designer. Again, all the pretty Photoshop images in the world mean nothing if they can't be reproduced accurately. To this end I always recommend either basic college courses covering the production aspects of design. Even if they are merely a couple semesters of community college and not a full degree. Or conversely, a year working at a print shop will teach the same aspects. I don't mean copy shops like Kinkos, but actual places with presses and ink.
Beyond knowing the production aspects for a chosen direction, any good designer should have an understanding of marketing as well. It is practically impossible to create an aesthetically pleasing and working design unless a designer understands the target audience. The designer needs to understand what is more pleasing to women vs. men, old vs. young, rich vs. working class. This all falls a but into psychology of sales - knowing what colors work for your market, what type sizes to use for the market, etc.
All of the the above can be learned "on the job" so to speak. But actually finding employers willing to teach you from the ground up is very difficult anymore. There are more and more young designers begin churned out of schools every year. According to Fox Business unemployment for arts degrees is rising regularly. If those with degrees, proving they know the technical aspects of design, can't find employment that simply means those without an arts degree are in for a more difficult struggle. I'd say that at least some college has become a requirement due to the popularity of the field in general. There's little reason an employer should "gamble" on an non-degreed designer if there are 50 degreed designers looking for jobs. Of course a truly outstanding portfolio can outweigh experience and degrees to an extend, but it is in no way an either or situation. Few get a job based solely on the portfolio, no matter how nice it may be.
If the intent is to simply freelance from the start, I suppose that's possible if expectations are set accordingly. Few ever get "rich" freelance designing. But it is quite possible to make a stable, decent, living in many cases. However one would need to start small, working on design part time while being employed elsewhere to pay the bills. From there it's simply a matter of finding and building a stable of steady clients who pay on time and return for more projects. Building that stable of clients can take years. However, I tell designers I speak to that once they have a minimum of 8 months living expenses saved and are making at least 60% of their monthly bills via design work on a regular basis, then it may be an appropriate time to look at freelancing full time.