Where do you see how many bitcoins are linked with byteball addresses? If it's possible to link exchange wallets or wallets you do not control directly it might be that most addresses linked are part of exchange's cold wallet. According to the official source, you can either make a payment or sign a message from an address you control. You're not bound to go with the second option since you can make a small payment.
http://transition.byteball.org/You can't link an address you don't control. Hell, if that could be done, I would simply claim all coins.
You have to make a payment from the bitcoin address you're trying to claim, or sign a message from it.
For your exchange example..... there is no way to know which address the exchange is going to pay with. Also, according to the site, if you claim an address via two diff byteball wallets, then the bitcoin address is ignored. So, even if you could claim it and someone else does, then the address is blocked from distribution.