Do you have any data on what the percentage of fatalities or maimings per capita before organized instruction?
Were they dropping like flies?
I did some reading on the earliest history a couple years ago. This is from memory. What I am writing is centered on the USA. I know little about the history elsewhere.
What we consider to be scuba instruction really started with the Scripps Institute in California in the early 1950s, and they created their version of scuba instruction in response to a diver death. When they created the course, they reportedly had no idea at first what to teach. They supposedly asked themselves what could go wrong and made up what they should teach for those occasions. A couple years later, Los Angeles County decided to make scuba part of their recreational program, and they sent one of their people (Al Tillman) to Scripps to learn how they did it. He came back to Los Angeles and made the Scripps system the Los Angeles system.
In the meantime, people were setting up as independent paid scuba instructors all across the nation, pretty much making it up as they went. The YMCA taught scuba, but each individual site had its own style of instruction.
Al Tillman and others in the LA program thought America needed a nationwide program. Since LA County's program was taxpayer supported, they could not expand it beyond the county. They brought professional instructors together from all over the country to see if they could form a new organization, with the biggest session being in Houston in 1960. A group of instructors from Chicago under the direction of a man named Dennis Erickson nearly took over and ran the resulting organization, but Tillman got control and became NAUI instructor #1.
They tried to run NAUI like the Taxpayer-supported LA county, relying on donations for primary funding, but it did not go well. In 1965, they announced that they needed to pull back from national work and focus on California, canceling a planned Chicago instructor training program. The Chicago group, still led by Dennis Erickson, responded by forming a new agency, calling themselves PADI.
So there really wasn't a lot of time between the invention of scuba and the creation of agency instruction. There weren't a lot of divers, and there isn't much in the way of statistical evidence from that time. The speed at which this all took place can be seen by an incident that took place in Australia in 1965 or 1966. A group of divers were planning a week of diving, and the boat captain announced that no one would be allowed to dive without a certification card. That only impacted one uncertified diver, who explained that he had learned to dive from his father and had done thousands of dives since then. The captain was unimpressed, but he eventually gave in and allowed Jean-Michelle Cousteau to dive without a certification card. (Cousteau is now PADI certified.)