I also always wondered why ^2 and not something else. What you pointed out gave me a possible hint at why, which was the simple, less computer intensive integer to implement without going unnecessarily too high.
I could be wrong about ^2 overall but I feel like it's better than linear for the reasons I pointed out or tried to point out.
True there were some abuses and I was very well aware of many but I feel like the free market would have regulated it over time.