there's a logical flaw in your argument, though, because where you say "we are trading for something that would be worthless anyway" it assumes the choice is between "trade secret" and "disclosed." But there is really also a choice between "trade secret, people know it exists and what it does but must guess at how" and "trade secret, no one knows it exists or what it does".
In other words, for some kinds of trade secrets, perhaps inventors might not even let you know of the existence of their invention, since without legal protection this knowledge would render the competitive advantage it confers worthless - even though before disclosure, skilled practitioners did not think to use it, as it is quite novel and those skilled in the art have not come up with it despite its obvious utility once disclosed.
Thus inventors might secretly enjoy its benefits or fruits. (This is easy enough to imagine; there could be a closely guarded manufacturing process in use right now that the public and other manufactuers do not even knows exists, and is not in the final product. The manufacturer simply makes an end product more cheaply, say. But telling us what the process is would give it away.)
Imagine, for example, that Google uses some kind of trade secret as part of ranking web pages. We don't even know what the process is, let alone how it is done. Naming the process would render it public and unprotected. So, it remains the only search engine that uses it, secretly.