You can’t sell code that already exists, you can only sell a license to use it.

In case of GPL it would mean selling users their freedom to use the software, because that is the only thing GPL license protects, right?

Therefore, I think that the only thing I can sell is the access to my version of the software, isn’t it? Once they buy it, it becomes their version with all the attached freedoms of GPL. It would be the access that I charge for, not the code.

On the other hand, charging for a web service is actually making a charge for providing something.

So I can’t charge for my work and time improving my copy and giving it away, but I can charge for a service that is, in a way, exclusive and proprietary?

I still fail to understand how charging for a service is better.