I don't understand why an exchange is a
risk. Let me explain my confusion in a real world example and then slap me with a dead fish and save my confusion please.
1) So, I want to buy my first bitcoins.

2) I find an exchange I like and wire them 1,000USD and let's say I get 2 bitcoins in return.
3) From my reading, I get a private key that I write down and stick in my favorite hiding place.
4) The exchange I bought the bitcoins from goes bankrupt and no longer exists.
5) I still have my bitcoin b/c I have the private key identifying my coin from all others
The only risk I see is during the 10 minutes or so of me wiring money and me getting my bitcoin key. After I get the key, I thought I am basically my own bank and the only protector in the world of that bitcoin.
Where am I off base?
Thanks.