No, actually. JS wasn't designed to be generally and minimally embeddable, it was a hack designed to be a embedded in a proprietary program with lots of bells and whistles. You can say that a thing doesn't have to be
designed for something to do it good if the users are crafty enough, but then what's the point? Python or Ruby would have equally served the role, none of the 3 languages were designed to be lightweight embeddable. The point about JS runtimes having more eyeballs and corporate support than most other language is fair, but the actual facts in OP make it moot : JS is used because of, what else?, legacy reasons. The decision was made in 2003-2004. That's, I think, barely after or during the first standard of JS, and when all the runtimes available were very buggy and divergent in behaviour.
In reality, there are plenty of interpreters you can embed and be very sure you're not making a mistake. Lisp and Forth are the top of that list, forth far ahead of lisp (literally designed to be used in embedded systems, and much simpler and lower-lever than most lisps). After that, there is Lua and Tcl, both explicitly designed to be embedded and extended, and lua specifically pushing words like "portable" and "lightweight" to the extremities. After that, you have Java (which runs on 3 billion devices!) and even Python, which has micro-variants running on higher end embedded Linux devices. JS is at around this tier.