It's a shame that doesn't exist. I've always thought you could make an especially strong argument for licensing for embedded software people, for many of the same reasons that a PE is licensed.

It wouldn't be a requirement for a job necessarily, but not a bad thing to have.

I doubt such a certification would have any correlation with ability. Maybe the platonic ideal of training and testing that you're thinking of, but not a certification written by the US government. Even competent parts of the government like NIST take forever to update their standards. It would be worse for a licensing bureau with practically no in-house software expertise.

You can get a computer engineering PE, which would probably be appropriate for the vast majority of embedded software developers. There was a software PE for a few years, but my understanding is that it was dropped for lack of interest.