Doable in principle? My impression was that the author doesn't argue against this. He claims it's unlikely to be doable in practice. That's the whole point of the article.
His argument is pretty poor. He refers to the threshold theorem which does rely on certain assumptions, and then claims that these assumptions cannot be satisfied in practice. This is apparently because "continuous quantities can be neither measured nor manipulated exactly", however this ISN'T an assumption of the threshold theorem. In fact the whole premise of the threshold theorem is that they can't. It's a straw man argument, the same one he's been making since the 1990s.
