The reality of the Scuba situation in the United States is that C-Card requirements are strictly enforced not by law, but by industry standards and practice. It isn't the law (thank God!) that requires a C-card to get air and equipment, it is the market - largely (whether we like it or not) driven by the economic forces of tort. There is no law other than the laws of common sense and reasonable care (backed up by the wording in the seller's liability insurance policy) that drives whether one can dive.
The temptation to draw parallels to aviation for scuba is appropriate in training and in the practice of the sport. But regulation is a different matter entirely. In aviation it is a public safety issue - in other words, regulation of aviation is there to protect the public from the individual aviator and his equipment, and any protection of the aviator him/herself is driven not by any public interest in his/her safety per se, but as a requirement to ensure the non-pilot public doesn't suffer from the results of the actions of the pilot - so the pilot must be healthy, competent and dependable. This isn't the case with scuba. There is no compelling state interest in ensuring the competence of scuba divers any more than there is the competence of swimmers or backpackers.
It is perfectly legal in the US for a person to buy their own boat, a compressor, tanks, regulator, BC etc and go diving to their heart's content. It is none of my business (beyond a duty as a fellow human being to encourage that person to seek proper training - but I have no claim of authority over his/her actions), none of your business, and (especially) none of the government's business. I know there are those who espouse a public claim on private risk-taking, but here, at least, we have a principle of personal freedom instead. Even the freedom to be an idiot.
C-cards are a convenient way to show a diver has received the requisite training to meet industry standards for diving. If we want a frequency/experience/currency standard then we already have that - it's called a logbook. If we want a proficiency standard we already have that too. It's called the "scuba skills update" or the "check-out" dive. And while I for one would advocate a worldwide raising of the bar before initial certification, and encourage shops and boats to take steps to ensure the diving competence of their customers, I would not direct it.
Rick