When people said don't trust exchanges, they didn't mean that you shouldn't use them. They meant that you shouldn't store your coins for long term in any exchange. Do your exchange/trading and then when you are done trading, move your coins as soon as possible. Don't use those exchange wallet as long term storage wallet. Bad idea. Exchanges might get hacked or your account might get compromised and you will end up losing everything.
As for webwallet, just avoid those at all cost. These are the least secured wallet where you can store your coins.
What's the long term in this case? What if I just deposited bitcoins and plan to store it for two days but tomorrow exchange got hacked and my funds are stolen? Once your bitcoins are gone, they are lost. Crypto isn't a bank's payment service where funds are under their control and if hack happens, they are easily able to get the money back, that's why exchanges need the highest security standards and well-written codes.
So, from the moment you send your cryptos to exchange, there is a risk that you may lose it.
But I have a question, why the f do I have to worry about that? If exchange got hacked, it's their fault, not mine and they should pay for any financial loses. That's why I think that PayPal and other top companies will come over current exchanges.