I think that by coding, you mean typing? In your example, we won't be eliminating coding, we'll just be entering code using a different language.
It could be possible to verbally configure the browser to use a proxy server and I guess that would be the different language you speak of. However, this leads to the need for AI or some kind of "intelligent" system: difficult to make one that isn't domain specific.
Though such an intelligent system is also inevitable (in my opinion), I think there is a step between describing software using such a system and writing code as we do today.
This step would be some kind of domain agnostic software framework that can be used to create software without the need to "code out" a solution. The framework itself would need to be coded, but the usage of the framework would not.
If you think typing in long programs is going away, you may be right - the future looks more like a Lego type of programming rather than the current sea of logical equations. But in that case I'd say you've coded your message in the form of lego blocks, but coding is still there in essence.
When you speak instructions into a computer, you've still coded. When you change your proxy like in your example, you've coded(in a non imperative way).
However, people will still need to know how to program (AI not being a factor).