The first main reason is that exchanges pay you an interest rate on your Crypto whilst cold wallets pay none.
Only some of them. Coinbase doesn't pay you anything. Some exchanges like yobit are really shady. Holding money on exchange in hope of earning 1% a year is really not my thing.
That's the way of saying exchanges that they aren't that really safe compare to cold storage but we can give you incentives for storing your assets to our platform. And yes, it may vary on the exchanges, some are offering 1% annually. If you really prefer having this, than safe storing then you can go with Binance, they are really the ones who made it first I think.
Secondly, we definitely believe that more and more users would move into hot wallets than using cold wallets, Ledger.com could become the next "Netscape" and then if your hardware device gets faulty and you would need support from Ledger.com - then you might find yourself in trouble. It's not a wild guess, this could seriously become the reality in the next few years.
If my wallet breaks I'll still have the seed. Do you have the seed for your exchange wallet?

Okay let's stop this which is which comparison, just weigh it personally, if you want your asset to have an interest like annual interest then go with exchanges that offers it, if you want to keep your asset on your own leave yourself a cold storage, these two have advantage and disadvantage and to be honest the security is in our own hands.