There is no reason to store funds in a wallet on an exchange because you can safely keep them in your own storage yourself. Holders of Bitcoin must know that when you need to exchange funds, only then do you transfer the amount that you require to be exchanged. Otherwise, keep the coins on cold storage with 2 backups, similar to how you would store gold in your house. An even safer route, open a safety deposit box at a bank for safe storage - it only costs $100 / yr.
No unregulated companies are going to hold on to my money unless for high-risk investing, that's mad!
Well, day traders are the only ones I see that should be holding funds on an exchange. Other than that, non-traders should be securing their funds in a wallet and not an exchange.
Agreed, though if you are a day trader - you must have any potential losses covered prior to entering the trading day. Otherwise, you could incur losses. Whether you are an experienced trader, or a new trader - it always helps to brush up on safe trading practices. The same formula applies to Bitcoin as it does to stocks. A quick Google for safe high-risk trading strategies should help any uneducated traders.
It breaks down like this:
"I have $200K in my wallet, on this day I shall transfer over $20K to the exchange and invest with this"
If the exchange has problems, at least you are only out 10% of your holdings.