Further with my theory:
It started as commemorating the Great Turf War.
Sure, being splatted hurt. But they felt that it allowed them to feel more empathy towards those lost during the war, and to those who survived their battles.
And some Inklings actually enjoyed the matches. So they pushed to make it happen more often.
Others liked watching it. Eventually it got ingrained strongly in the culture.
Inklings got paid for their participation like normal athletes. Because it was profreshional sport.
And the long term negative effects were discovered too late, after it was strongly in the society.