Who is a professional writer?

In my college training to become a professional teacher, I was reminded by a professor that a true professional is something like a hired gun. Paid to bring understanding and edification to a group, a professional teacher, using his own skills, must teach what he's being paid to teach.
Using that standard, a professional writer would be paid to write what readers demand, would he not? Employing all the skills and devices at his command, the writer would write cozy mysteries if that was most in demand; or historical romance if that the hot button of the day.
Where then, does that leave the writer who knows what's in his head and his heart to write, regardless of whether it is popular or not? Assuming that writer uses equal skill and devices, would his work not be the equal of the other?
This is not rhetorical. I honestly do not know the answer. In fact, I was never able to blithely accept that professor's assertion at face value. When I was active in the field, I often found myself challenged by local citizens who wanted my band to play nothing but Sousa marches, or sports addicts who insisted my band play only pop tunes 'everybody' would appreciate. Where, I asked myself, did the musical education of my students enter that picture?
In much the same way, I find myself tempted now to fill a burgeoning market; one I've been assured will bring me more sales and spread my reputation as a fiction author. Therein lies the rub--that the reputation I want spread is that I have something significant to say to my reader. If I'm only a diversion, a few hours of distraction from the cares of the world, why should I care?
Chime in here. Tell me if you think I'm going wrong. I read and consider every comment that comes my way and I appreciate those of you who have shared your thoughts. I hope you'll continue to do so.
Cheers,
Pat Dale