With lawyers (more familiar there than with doctors) I don't think that's usually the case; the ABA model rules don't prohibit lawyers from being supervised by non-lawyers (though they do prohibit lawyers from co-owning law firms with non-lawyers, or sharing legal fees with non-lawyers, and they do prohibit lawyers from allowing their employer to "to direct or regulate the lawyer's professional judgment" in providing legal services -- whether or not the employer is a lawyer; this doesn't prevent supervision of the lawyer as an employee, it just essentially means that the lawyer doesn't have a Nuremberg defense of "just following orders" for professional nonfeasance or misconduct.)
http://www.americanbar.org/groups/professional_responsibilit...
I've supervised lawyers, though I'm not a lawyer. I know the same applies to other people with regards to doctors. The trade establishes rules they can't violate, but there are a ton of caveats on that. Regardless, those restrictions are actually needed by the organizations for specific roles. If a programmer was needed in a similar way for a specific role, it'd largely work out the same way. The main difference is there'd be no independent review board that has no idea what is going on in the day-to-day unless otherwise alerted.
The prestige/pay/working conditions thing is more a result of a trade group, and the consequent standards for people even being part of the trade, than due to supervision by those who lack skill expertise.
If you restrict yourself to the subset of programmers who have similar education, training, and professional validation processes as doctors & lawyers, I think you'll find a lot of prestige, pay, and quality work conditions (lawyers and doctors will tell you that it isn't quite as good as you imagine anyway).
It's considered unethical for doctors or lawyers to have their work supervised by anyone who isn't a doctor or lawyer. They enforce the rule through professional conduct rules and boards. the result is very high prestige, pay, and working conditions for people with similar skills and education to programmers.
But the atomistic libertarianism and lack of solidarity among programmers makes us targets of mass low wage immigration, outsourcing, and every kind of unpleasant work situation.