The optimization is unsound. 

The JIT compiler is sound, w.r.t. to the source language's semantics. That's the only thing that matters for the programmer.

   but it's inelegant.

Elegance is in the eye of the beholder. I was blown away when I first encountered JIT compilers.

  lack of powerful static analyses

That's an orthogonal issue. More powerful static analysis is also more time-consuming. One of the design goals of Javascript JITs is to make web-pages as responsive as possible. That rules out complicated static analysis.