I was looking at the rules and I got a little confused on why it's only allowed on Xbox. Can someone clear up the reasoning?

Allowing HDD on Xbox was done to prevent issues that had arisen from playing on disc from getting out of hand. What was found to be the fastest disc drive had occasional slow loads and also burned rings in discs. In addition they made lag clips, an optimal strat at the time much more difficult and it was found that purposely smudging and even defacing your disc could make them easier, which was a slippery slope. Allowing HDD on Xbox was basically an easy way to mostly standardize loads and to avoid going down the disc-defacing rabbit hole. The other two consoles have no such issues with using a disc and thus there’s no reason to allow it, besides using HDD would still be slower than Xbox anyways. These videos explain it in more detail