You could send those particles in parallel though (i.e. make your channel wider in information theory). More particles should not take more time, just more space, which is fine. I was also puzzled by this sentence in the article.
It's not puzzling. It's a statement of faith, not something that has a solid theoretical basis.
Any form of FTL causes problems with causality - or at least with current assumptions about causality. So physicists tend to work back from that to "Therefore this is impossible."
But those assumptions may turn out to be wrong and relativity may be violated in specific quantum contexts. And then all kinds of interesting things happen.
Incidentally, this is an example of the kind of thing Hossenfelder was talking about. You could spend $20bn on a new collider, or you can spend a couple of million - at the absolute most - to check there's nothing unexpected happening here.
It's a wild bet, but given the up side it's hard to characterise it as poor value.
At worst you'll get some insight into the interface between QM and relativity, with another situation where Relativity Wins Again - but you understand why, in detail.
At best you'll get something more challenging and interesting.
