Regarding performance, one thing to keep in mind is that all of the languages you mention use GC, which can help with cache locality issues. In Rust, of course, the situation is different. Gankro also addresses the common and useful idioms you see in most functional languages through corresponding vector-centric functions on the Rust side. (Scala is perhaps a reasonable midpoint.)
That all said, I too would love to see some substantiation of the performance intuitions here.
I think one of the problems here is that the discussion of how bad linked lists are switches back and forth between taking about Rust specifically and linked lists generally.
Also, I think performance claims, especially ones as strong as the ones in that document, should be avoided without substantiation.
It's still a bit of a draft document (still missing the last chapter, for one). Happy to change stuff based on proof. That's one of the more dubious ones for sure.
That all said, I too would love to see some substantiation of the performance intuitions here.