Why isn't there a strategy to grab the private key from the exchange. After all the bitcoins are mine. Are there ways to do this? As in, in case something happens to the exchange like Mt Gox. Why is the key accessible to a hacker but not to the owner of the coin? Why are there no exchanges giving users private keys?
If you want to have full control over your coins, then you should only store them in a self-custodial wallet; that's only how you can be in full control. Centralized exchanges don't generate private keys because that's how they are designed. If you have some coins on an exchange, what you can be more concerned about is your log-in details, which you must keep safe.
In the past years, a few exchanges have been hacked, and investors who had their coins in those exchanges lost their funds. If exchange allows each user to have a private key, then it may be difficult for them to run smoothly.
It's not a feature that can not be initiated on CEX; if it were possible, then it would have been done since, so don't even think of storing your coins on any centralized platform because it's not safe enough, as long as that coin is not in your custodial wallet.
