I too do not understand why I was taught that the safety stop was mandatory on dives deeper than 30m.
It is still the official statement when using the PADI RDP.
Before the PADI RDP, people used the Navy tables, and they were really not the best for recreational dives because they called for extremely long surface intervals. Most Navy divers only did one dive a day, so it didn't matter to them, but for recreational divers trying to do a two tank dive with AL 80s, it was a problem. PADI did extensive research on the kind of diving done by recreational divers and found that for people doing such dives within certain parameters, it was quite safe to use a system that led to shorter certain intervals, and they created the PADI RDP to guide such dives. Their goal was to create a simple dive table that could be used by that kind of diver under those circumstances.
The more complicated Navy tables went beyond those recreational limits and introduced decompression stops at certain depths and times. The need for such stops increases gradually with increasing depth and time. PADI wanted to produce a table for dives that did not require those decompression stops, and that is what they did. They did include the idea of a safety stop to be, well, safe. These were physically the same as decompression stops, but they were taken at depths and times that did not normally require decompression stops in the Navy tables, so they gave them a different name and said they were just recommendations.
There were times, though, that divers were really close to the depths and times when decompression stops were going to be required. With the goal once again of being safe, PADI decided to make the stops mandatory then. These really were decompression stops, but I suspect (don't know for sure) that they decided to stick with the safety stop language for simplicity, saying that they are recommended in some cases and required in others. Dives to 30 meters (100 feet) are among the reasons for a safety stop to be mandatory. It is really a decompression stop, but that is just language.