I know everyone loves the "it's a free country, we can't sto them" argument. In general, we have many freedoms extended to us in the United States, but they are generally only extended until we begin to infringe on other's freedoms. For example, I am free to speak, but if I go into a courtroom and exercise my right to free speech while the Judge is speaking, I will be rightly thrown out for interrupting the process. I infringed on the free speech rights of the Judge, and my right to free speech in that location was temporarily revoked.
In the same way, we are allowed to drive with licenses. However, if in our driving, we strike another vehicle, then we have infringed on their right to drive, and have destroyed their property, and we are fined or lose our license.
Once you infringe on other's rights, you often stand to be punished or lose your own rights. In this case, open water divers in caves are on the borderline of infringing on other's rights. Recovery divers have lost their right to freedom as they must submit to their pledge and spend their time recovering the body. They are at risk of losing their right to life in the pursuit of this person's remains. All of us stand to lose our rights to cave dive as a result of this mans actions.
Batons? Cave police? No. I have already suggested what we should do. Stop supporting untrained divers. Fill station operators should start checking certifications and listening to customers. People talk. It's not often very hard to know when an untrained diver is diving in caves. Case in point, a fill station operator in North Florida was telling me about two Intro certified divers who are mentoring/training their OW friend how to cave dive. He still fills their tanks, even though he knows what they are doing. I think that shop should stop filling those persons' tanks and let them find another fill station. Lots of people knew about my two friends, or atleast suspected, what they were doing, and only some of us tried to stop them. I didn't try hard enough, partly because I didn't know the full story. I could have dug around to get more info, but I didn't.
I was trying to explain to a user who PM'd me some good ways to stop this. What it comes down to is, perceived cost. These open water divers apparently perceive the cost of cave training to be higher than the cost of diving without training. Education, via signs, or via open water classes, might increase the perceived cost to these people. If they knew that they would be shunned by the cave community, that might also increase the perceived cost. Peer pressure is very powerful.
Some fully trained divers do not belong in caves. There are cave instructors with a reputation for passing people who fail to meet the standards of other instructors. I don't know if you know much about cave country politics, but there are instructors that have a smellier reputation than horse poop. Word gets around, and I'd like to think it reduces the number of students those poor instructors see.
Curriculum is just the books, so you are right. When the curriculum allows for an instructor to be done training in just three days, though, I feel that allows for more instructors to make the decision to shorten training. If curriculums required a minimum of double the current number of dives, over a 6 day period, then I feel that gives more time for the good instructor to do a good job. There are some instructors who don't even have class time, all learning is done online. Those instructors never even have a chance to play videos showing the dangers of caves.
No matter what, someone will die in caves. But, I feel that giving up and accepting that fact is not a good option. We should do everything we can to create a climate in the dive industry and world that minimizes the number of divers who die in caves. We've made progress since the 70's, but we need to do more, and as you all point out, it's getting harder to do things. Rule of diminishing marginal returns.

But 4 people in less than 3 years? I think more uncertified divers have died inc aves recently than trained divers, a reversal of the last decade's trends. Perhaps someone who has perused the statistics more recently than I can weigh in on whether I am correct? I think it's close to equal (trained vs. untrained deaths) and I think for several years, trained deaths were outnumbering untrained.