Sure, but rust benefits from must_use annotations, which effectively turn those annotated affine types into linear types. Turns out they are both useful in a very overlapping venn-diagram kind of way.
declare x (must_use);
P;
use(x)
(I apologies for the non-Rust-conforming pseudo-code.) The type-checker won't be able to tell if P terminates or not, whence x's use can't be enforced. That's a direct consequence of Rice's theorem (which in turn follows directly form the non-computability of the halting predicate).