Probably to avoid minor scratches and injuries from contaminating the floor with blood, which would require nanny-state cleanup squads to interrupt the flow of the tournament. These days it's all about advertising revenue and the less appealing the end result is to TV broadcasters, the less money comes in from sponsors.
Other sports have had rule-changes to make them more appealing for TV, so it's nothing new.
Basically this. The idea is to avoid injuries to the hands and feet, and also to try and minimize injuries to the face. Tournament sparring is also a huge draw for kids, and parents tend to balk at seeing their kids bloodied up in a match.
Ironically, all of that padding can actually be very counter-productive especially for children. You avoid cuts and busted knuckles - but at the same time you significantly increase the amount of force that people are willing to trade; and you increase the amount of rotational force that can be applied to the head. That is, the padding can sort of "catch" on the head and force it to turn, much more so than a bare fist would; and the rotation of the skull is actually more dangerous over time than the cuts and bruises you're avoiding with the pads. It's even worse when they wear those padded helmets.
It's the same reason that MMA is ultimately safer than boxing... people get blooded up a lot more, and maybe break a bone or tear something... but boxers end up with brain damage. The gloves allow them to punch much harder, and transfer a lot more of that energy to the brain.