But to what level do you reduce the complexity of 'doing' something? If you agree you do not have to be paid, do not have to have a specific regularity or timetable to your work, then where do you draw the line to say someone is not part of a profession.
As an example: A man who stood in his backyard with an old telescope and made observations and study of the night sky, however irregularly, even monthly or less, would be called an amatuer astronomer.
Someone who did the same, with a masters degree, and slightly more precision would be called an expert astronomer (not professional ofcourse). Even if they only make the most meagre of study and observation.
The above is an astronomer. Academic study in this case is definetly enough. Amatuers regularly make major discoveries.
Now, how is this different from my previous example of someone who provides free legal counsel in an informal fashion calling themselves a lawyer? Are you proposing they need to be employed within a part-time or full-time framework, a number of hours per week, to claim they are within a profession?
No.
So electricians, plumbers, mechanics, chefs, tradesmen of all sorts who own their own business are not entitled to claim this as their role, just because they are self employed?