You are not being deprived of any rights. You just don't have them exclusively. Make music, or don't. Up to you. Either way, there will be machines also making music. So, what?
Now imagine in a group of people you share a hand-crafted song but one of your friends who isn't as interested in producing music takes your song as inspiration and creates something that sounds better. Imagine they aren't even trying to do this to intentionally one-up you; they think of it as the same kind of sharing and creation. You may disagree but their definition of self-expression differs, and it's difficult to change people. But this happens consistently and the bar is raised ever higher each time.
How well someone handles this kind of scenario depends on mindset. Is the joy in being better than others, or pursuing the craft and learning things, or sharing in the experience in consumption? People will have different values. But I think the bias in AI is for people to focus on the end result without needing to put in a lot of effort.
It's the entire selling point of these products - taking out the effort in getting a high-quality result. Yet the effort spent on human art isn't wasted effort. The effort doesn't just go towards the finished price, but to the satisfaction of the artist themselves. It stimulates their neurobiology. And in a lot of tutorials for hand-crafted art, the mindset taught is to focus on the process and not the end result. Generative art contradicts that bit of knowledge, and it could cause dissonance.
In Stanisław Lem's story about the electronic bard, the existence of the impeccable poetry-generating robot does not directly deprive the poets of their ability to create their own poems. Instead, after perceiving the generated work to be higher quality than anything they're capable of writing, the poets become depressed and commit suicide.
You could say the poets didn't have the right mindset of how to approach life, but I think it raises a good point. It's the mental state of people who create and how society views these tools that matters. You will always have the ability to put pencil to paper regardless of what big technology does, but will you want to if you think the rest of the world has moved on without you?
I think maybe in modern times the effect will be closer to: artists scale back or give up their craft because the potential audiences vote with their wallets and attention spans for people who rent server farms. It's the despair at seeing the public valuing the end-result over the human element in a broader cultural sense. It's feeling as if a piece of yourself is being lost in an eternal void.
And it's the idea that generative models could become a fundamental part of society. Billboards are generated because those cause the most successful ad campaigns. People hold massive music festivals exclusively made of generative synth lines because they attract the crowds. The taste of your drink is algorithmically modeled with ingredients adjusted for the best product-market fit possible.
What stops these people in their tracks is perceiving the world as one that values the machine over the human, and even if you value the human, you still have to get in line with the machine - everyone else is doing it. Generative models could retrain our value systems.
It's not so much what generative models take away than how they change the public's perception of art itself. It is the depression and mindset changes that come with knowing the poetry-robot will be there for all eternity.
Older forms of thinking become outdated, some which may be considered virtuous or delicately intertwined with the human spirit, and this causes anguish and despair at the state of things, and the ever-improving army of poetry robots that sees no end in sight. Because we haven't put an end state on improving technology, and I think deep down some of us believe there was never meant to be such an end state in the future. We would have to spin terms like degrowth and Luddism into something more palatable to have any chance of creating one.
Oh, maybe because watching live music is a different experience. Maybe because being the best is not as important as simply doing something most people can't do.
Funny thing is, when you go to shows of people who are not yet professional musicians but might be studying, might be in a band with their friends and so on... most of the people who attend these shows are their friends and also other musicians. Most musicians are not professional musicians.
But there still are people making art with older techniques. There is a greater variety of art being made today than ever before in history. The development of new techniques has made art richer rather than poorer. Yes, the most commercially focused art chooses techniques based on price (far cheaper for a single person to stack synths than to pay a full orchestra) but that's okay.
Hip hop and electronic music have been creating totally new things for decades without ever touching a physical instrument. Music didn't die, it flourished.
I'm worried we're going to go into a dark age where society forgets how to make truly creative new art due to lack of incentives, and the AIs won't make anything new due to lack of anything creative to train on. We'll just regurgitate the pre-AI stuff forever.
This is not a slippery slope; new art will be created regardless of incentives and skilled people who learn to augment their craft with AI will probably create better works of art.