IMO, variables being const/immutable by default is just good practice codified in the language and says nothing about Rust being "functional-first":
Most variables are only written once, and then read one or more times, especially so when you remove the need for manually updated loop counters. Because of that, it results in less noisy/more readable code when you only need to mark the subset of variables are going to be updated later, rather than the inverse. Moreover, when variables are immutable by default, you cannot forget to mark them appropriately, unlike when they are mutable by default
I did enjoy this comment:
In other words, a small subset of C code is more trustworthy than Rust code written by "some confused n00b". Which I would argue is quite the feather in Rust's cap