Idris 1 compiles via C, it just has to implement a garbage collector in its runtime system. It should be noted that Idris 1 has much worse performance than Idris 2 compiled to Chez Scheme, it would take a serious effort to do better than the current Chez backend.

The logical target for a high-performance backend would be LLVM instead of rust. After elaboration Idris 2 has a series of intermediate languages, from lambda calculus to a simple register machine. Creating LLVM code from the least abstract of them wouldn't be any harder than creating Rust code.