Agreed.
> So the question is on average are these statistical regularities better or worse than those introduced by the alternative,
Indeed. This is an empirical question. That is what the article is about, for a specific setting.
> ... and the answer is no, if implemented properly.
I don't agree with that. This is not about implementation. It's about how the statistical regularities that are imposed on the full output distribution affect that distribution. There is a change - by construction. That change can be good in some situations and bad in others. The authors claim that it is mostly bad in the setting that they investigated. This looks like a fair statement.