You don't care with it because you have no choice and you have to comply so that you can get your money. If you won't comply to their KYC implementation, you will let your money sit on them forever so that's why you need to take actions with it.
Why they want our info? same with the exchanges, it is either they are following a strict rule from their country that if ever someone wins a big pot, they have to send reports about that to their gov't including the identity of the winner.
That could be dangerous if an insides decides to get greedy and make a plan to steal the price he/she earned, otherwise it's not really that bad.
It's a security measurement they put in place that helps but it's far from being a perfect solution. Especially because people just buy the documents of others and a lot of people in some sites is willing to sell them really cheap.