Granted. But even so, the primary problem is that the input is infinite: we can deal with any finite input stream, no problem.

ETA: Also, the obvious way to approach the problem is to have a terminator character (this is how the unary representation works, for instance). In that case, what this result says is "if your decoder expects a terminator, then if you feed it an infinite string without a terminator, it'll get stuck." This seems obvious.