I think OP understands that.
And I think OP's point, more succinctly, is that Valen programs will be much more difficult to parallelize than Rust programs.
It's shockingly easy to make a single-threaded Rust program use all the cores on a machine by slapping in Rayon wherever you have a Vec. Because Rust forces you to do the hard work of proving shared^mutable before getting a single-threaded program running.
The ecosystem-wide consequence of this is that pretty much every compute-intensive program written in Rust (that doesn't rely on non-Rust libraries for compute-intensive stuff) is automatically multicore. This is one of the reasons why Rust programmers seek out Rust libraries first. Because they know they won't get the unpleasant surprise of putting in a lot of work to adopt a library and then get burned when they find out it will only use a single core.
How widespread are locks in typical Rust code?
Apologies for not understanding. And I admit, it's hard to communicate in the abstract, so I might still not understand the question.
If it helps: AFAICT, Valen's borrow checker preserves the same ecosystem-wide concurrency benefits that Rust has. For precedent, check out GhostCell [0] which is not only _compatible_ with Rust's concurrency but gives it some interesting new abilities. Valen's approach could be thought of as a more ergonomic form of GhostCell that better tracks the relationships between multiple groups (brands).
I could give a better answer if we had an example to toss around where we think Valen might force things to be single-threaded.