This could easily be the case for software engineers too, if we didn't abdicate the power to judge competency to employers and vendor certifications.

Of course all established engineering fields are incredibly narrow compared to the scope of what software might conceivably do. There are simply no definitions of software fields that have the rigor for such objective evaluations and licensure. And there probably never will be given that the substrate of physical engineering is physical matter with unchanging properties whereas with software it's a ponderous stack of man-made abstractions.

It doesn't mean that programming is in any less need of rigor or that it is any easier than any other form of engineering at scale.

Only in some countries. In others, anyone can profess to be an engineer.

You realize that in most US states, software engineers can now sit for a PE license in software engineering, right? This has been possible in a few states since 2012, when the NCEES started offering the PE license exam in software engineering.

This is the same license that electrical, mechanical, structural engineers get, with the same initial Fundamentals of Engineering exam followed by the subject matter (P&P) exam (usually after verification of a certain amount of experience).