The private key is publicly known. But why all the double spends?
You just answered your own question. Because the private key is known, the instant anyone sends coins to that address, somebody will attempt to transfer those coins to their own addresses before anyone else does. But since everybody else has the exact same plan, the result is a great many transactions from many different people all trying to spend the same coins.
I thought of this but had the idea someone will get their transaction first (maybe a few milliseconds quicker) and that one would be accepted. All the rest that followed would double spend.