Consider, for instance, that between 1935 and '37 the World Chess Champion was Max Euwe, whose main employment was as a maths teacher.
Professional? Or amateur? In Go, this sort of question doesn’t appear as much.
Howard Staunton, unofficial World #1 ca. 1843–'51, was an editor of Shakespeare – professional? Or amateur? Can we imagine Honinbo Shuwa, say, publishing commentaries on haiku? Sometimes Ota Yuzo (Shusaku’s rival) is called an amateur because he never played in the Castle Games, refusing to shave his head, but Sensei’s Library is currently calling him a professional.
The question really goes back to this core issue of “In a time when it’s logistically unfeasible to maintain an Elo-style rating system, even if the concept was understood, how do we work out who is “strong” at the current time, so that the strong players can compete against each other?”
In Japan, though, the idea of a professional became that they were “artisans” or “martial artists”, whose association with amateur players would somehow sully the purity of the craft. This attitude definitely still lingers – otherwise, why are Japanese professionals not permitted to compete in amateur tournaments?
My “controversial opinion” on this topic is that Europe and America should have never introduced an imitative split between the “amateurs” and “professionals”, which isn’t necessary in the 21st century or rooted in our native culture or extant organisational Go structure. A strong player should be considered just a “strong player”, given a rating and dan rank, and not assigned as an “amateur” or “professional”.
Similarly, there’s no need for an exclusive European or American “professional league”, only an open qualification system accessible to these uncategorised “strong players”, who will be competing in national championships and large swisses like the London or Paris Open. My impression is that Western organisers wanted to mimic Oriental systems without properly considering whether they were appropriate, necessary, or helpful.