When combined with a pro-capitalism platform, you might be right. If writers need copyright to be able to eat and pay rent, then you are right.
But anti-copyright, combined with an anti-property ("anarchist") platform isn't necessarily anti-civilisation, or anti-intellectual. Other structures, like syndicates, architecture, designed artifacts, and other forms of culture, can provide "civilisation".
In such a society, writers (and everyone else) would be born with the right to a fair share of the living space and food around them. They would be expected to contribute a fair share. As they got better at writing, people might start to agree that their time was better spent writing than in the fields, and would petition their work syndicate to post them as a writer.
(Of course, this is anarchism, so they could just go write the books anyway, they would just lose social standing if people felt they weren't contributing their fair share.)
You might say that creators wouldn't create if there wasn't a carrot of Wealth dangling out in front of them somewhere.
We can debate that point. I'm interested to hear your thoughts. But in my experience the great creators of culture who I know well do it despite the monetary consequences, not because of them. They write themselves into poverty... orchestrate music into the middle class... paint on a teacher's salary.
And yeah, some of them become insanely wealthy. But I don't think the majority of them do it for the wealth. If they do, that would be very stupid, no matter what system you're in.
Give everyone the basic necessities in fair trade for contributing to the syndicates that make their food, housing, and health possible, and I think you'd see an explosion in creativity, not the opposite.
I don't think that is ever true of anybody. A writer needs to read 10, 100, 1000 books before he can produce a book of similar quality. The same applies to musicians who learn from other people's music, painters who learn from other people's paintings, and scientists who build upon other people's work. Nobody creates IP out of a vacuum. If anything, creative people are even more indebted to other people's IP than simple consumers are.
The question is: To what extent? If we measure how much income a person have from intellectual property and how much money they spend on intellectual property (if they not steal) then you will see the following:
Most people are only consumers.
A fraction of people create things as a hobby, so their consumption is not much smaller than their production.
A tiny fraction of people produce intellectual property for a living: their consumption is tiny compared to their production.
If you are in the first camp then in short term no-copyright may be good for you. But if you are in the 3rd camp, it is bad for you, because in that case you are 99% producer and 1% consumer of these kind of goods.
That's why I think that the no-copyright movement is unfortunatelly partly an anti-intellectual, populist, 'anti-civilisational', (ok, maybe anti elitist too) movement: the less creative people's fight to take away rights from more creative people. (And creativity is only partly talent, it is also really hard work, so this movement is against hard intellectual work.)