Yes! One should not keep all coins in an exchange since it is very risky. We dont know if it is still there tommorow as we wake up. And although some exchange are very secure still there are lots of hackers that are willing to steal your coins. All i can advice is to invest what you can afford to lose.
That is very risky if you don't know the exchange that you will put all of your coins but if you trust them and they have valid permits from the government where they are basing.
I guess that is going to be a good way to trust them and put your all your coins to them and they have a legit and physical office.
But if you are just using an online wallet and you are far from them, then don't just put all of your coins.
Even if you know the site, it's still not advisable to put all your money in exchange sites. Even in real life, when you have a bank deposits you do not put all your money in one bank.
In our country, there is a limit of insured amount so if bank will close and I have more than the limit then I am a loss.
Say for example, I have 10 million dollars, I need to deposit that amount in 20 banks or 20 bank accounts if bank will allow different accounts in one bank. This example is based on the insurance of $500,000.
This is just an example to qualify the above suggestion..