It a little tricker than that. Both Rust and C++ can auto-execute code at the end of the scope of a block of code (stack level destructors). So you would still be imposing extra work on the programmer to use a Rust back-end exposed through a TypeScript front-end, and you'd end up with an exposed API exactly the same as the current TypeScript version.
I'll still pursue the Rust implementation, mainly because I've already invested the time/effort in learning it real well. And I find it an interesting language. As for work projects where productivity is important, Kotlin looks more attractive to me if your existing code-base exists on the jvm.