Would that be so bad, in the grand scheme of things?
But you're right, it generally requires you have a 4-year degree and have worked under a licensed engineer for some number of years.
Them hiring only people with degrees is almost certainly orthogonal to legal requirements in such cases.
Any sort of professional interaction with patients, sure, whole different ballgame.
Components at every stage of the design and manufacturing of a commercial airplane are signed off by licensed engineers who are legally liable for negligence, and yet Boeing could outsource the 737 Max's software to $9/hr programmers in India. Obviously physical engineering failures still happen, but it's ridiculous that there's no liable professional responsible for software that keeps a plane full of hundreds of people from falling out of the sky.
If a licensed accountant was caught lying about hundreds of people stealing from their employer to the point of getting some sent to jail he could easily do jail time for negligence or perjury. Instead some seemingly anonymous dev wrote shoddy software that ruined hundreds of lives and the Post Office gets to just say that the computer did an oopsie.
Moving safely means moving slow, and that costs more - it's as simple as that. Plus it would also automatically disqualify like 80% of the workforce, due to the need for a proper formal education and certification, which would literally paralyze the industry.
And the current solution is not that different from what we have e.g. in civil engineering, the building codes for high-rise buildings are way more strict and complex than the regulations for a garden shed - in many places no permit is needed at all for it. And sometimes that means that that shad will fall in a catastrophic way, too.