They may pay well but most non-computer engineering grads I know end up in software because that's all that was available.

I really think you’re just living in a bubble. I know many recently graduated non-CS engineers who stepped straight into high salaries in their fields. Civil, mechanical, structural, aerospace, petroleum, acoustic, chemical, material, biomed, marine, geological... There are literally hundreds of different specialised engineering disciplines, and so many of them are high-demand and high-paid. Don’t get all your information about the world from SF job listings.