From what I understand the only defense against this event is to divide your assets into many accounts to reduce the risk.
No, the defense against this is math:
Let's say we have a trillion planet Earths. On each Earth, there are a trillion people. Each person has a trillion computers. Each computer generates a trillion keys a second. All these computers have been creating a trillion keys per second since the birth of the universe 13.7 billion years ago. 10^12 * 10^12 * 10^12 * 10^12 * 60 * 60 * 24 * 365 * 13.7 * 10^9 = 4.3*10^65. This means thay they would have so far generated approximately 0.0000000004% of all private keys.
If you are worried about someone using such a site to stumble across your private key, then you should be absolutely terrified of dying from a meteor strike, shark attack, or lightning strike, all of which are exponentially more likely to happen. You should also be terrified about someone guessing your credit card number and stealing all your fiat, since for every possible credit card number there is somewhere in the region of 10 trillion trillion trillion trillion trillion possible private keys.