I can agree with that. We have stuff like fan fiction which people write and share for free. I guess 50 Shades of Grey is the preeminent example of writing as a passion and as a calling rather than a professional skill.
There are authors whose main body of work was only published after their deaths and who are considered literary masters nonetheless, and not fanfiction writers.
All in all, I agree with a sibling comment: we must divorce the business of writing with the art of writing. They are related, of course, but the latter doesn't require the former. Once one understands this, one is less inclined to claim things such as "if writers don't get paid, books won't get written".
That is kind of the definition of professional though.
Writing, like any other skill, takes time and practice to master. If you can't dedicate yourself full time you will not reach your highest potential. And it requires some form of income to be able to dedicate yourself full time. Just like a professional pianist will be better than an amateur.
The second sentence here doesn't really follow from the first. I mean, assuming that only time and practice are needed for mastery, then practicing less-than-full-time only makes it correspondingly longer to reach mastery - it doesn't make it impossible, like you claim.
In reality, time and practice are not the only factors, though. You have to account for talent, which not only sets the upper bound on the quality of your writing, but also influences the rate of improvement with practice. It's not exactly unheard of for a debutant's work to be "way better than the latest work of established master X", isn't it? Talent is hard to capture and define, but it's a real thing, especially in the arts, although it also plays a part in trades and crafts (that's where the "10x programmers" and similar concepts come from...)
Getting paid by publishers for writing books is a powerful motivator, but not the only one. In a world without a way to sell books, writers would still write.