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The type of hot wallets exchanges use are mostly HD wallets therefore. It's not just one address whose seeds are going to be exposed. It will be thousands of address of different accounts and by trying to recover only $10K. Risking millions of people's asset because of 1 person's assets that's not even listed in the exchange is a no-go area for most exchanges.
Ok, maybe I don't get something simple. I have one ETH address in my Kraken account unique only to me. Blockchain tells me, there is only my mistakenly sent PaxGold on this address (listed on Kraken btw). Every address has one unique seed attached to it, correct? Can't Kraken just go to My Ether wallet, enter private key or seed and access my funds?