Not an expert, so a more nuanced view may help, but from my understanding, developing an ASIC even for a simple task is a lot of work. JavaScript is already optimized to run on a CPU. It has many different general roles as a language itself, and making an ASIC for JavaScript as a whole would basically be making a CPU itself.
Typically, you don't run a general code engine on an ASIC. They're more for a specific application, where it can do the job it was hard designed for, which is why they're so fast and efficient
