Your analysis sounds reasonable to the non-expert, but recent work on purely-functional trees suggests that the gap is smaller than you suggest ("orders of magnitude slower").
E.g., see the nice work on the PAM library (https://arxiv.org/abs/1612.05665). Ideas from this work were used to build lots of cool things (immutable graph data structures, segment trees, databases) that are very fast, and all immutable.
This shit is all lies dude. In measurements like this, they constrain mutable structures to the same memory layouts and ideas as immutable ones and say “see! Sometimes kinda close!”
> bog standard FP community lies
> constrain mutable structures to the same memory layouts and ideas as immutable ones
What are you even talking about, "dude"? I don't think you have the background or knowledge you seem to think you have to argue about this space. It's OK, as you blithely pointed out in your earlier post, there is a place called medium where you'll find likeminded folks that will eat up your drivel.