So if I'm understanding this particular tussle correctly, carry flags are problematic for optimization because they create implicit mutable shared global state, which isn't necessarily reflected in the machine code.

Risc-v basically says "lets make the implicit, explicit" and you have to essentially use registers to store the carry information when operating on bigints. Which for the current impl means chaining more instructions.

Is that correct?

That sounds like what the FP crowd is always talking about - eschewing shared state so it's easier to reason about, optimize, parallelize, etc.