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.