Yes, if everyone can produce as much of it as they want, then it would lose value. However, someone doesn’t need to back something for it to have value. The most common currency in all of history was seashells. Nobody backed the seashells. Gold has had value for a long time and still does. Nobody backs gold. The reason these things had/have value is for a number of reasons, but possibly the most important reason is what you said, that nobody can just produce as much of if as they want. This is also a fundamental reason why Bitcoin has been steadily increasing in value, nobody can produce as much of it as they want. This is a major flaw that is inherent in fiat currencies(usd, euro, lira…), they can be produced as much as somebody(governments, counterfeiters) wants.
This is very simplistic, there are other reasons that various things are good ways to hold value. Divisibility and transportability are two big ones, both which Bitcoin excels at.
It also makes a way for the poor to be able to afford to get art to make comics and other things when they otherwise would have been unable to hire artists. Generative ai also allows poor people to write code they couldn’t before because they couldn’t afford the help. It also gives poor people the ability to brainstorm new ideas when they can’t afford a team of consultants.
It helps the poor, just like search engines and the internet. There were people back in those days scared of change as well. Gen ai is a huge equalizer or wealth and power. The vast majority of people using Gen Ai are using it for things that they never would have considered being able to hire someone to do anyway.