Not your your key not your coins and this quote is the forum main tag line.
As always and considering it as a golden rule, IMO. I also repeatedly say this to anyone who needs advice.
With the current market situation, where the bear pushes the dip further, chances are most centralized exchanges are being forced to go insolvent or even shut down due to inability to meet up with government taxes. And should this happen, your coins are at risk. Either you lose it all or get compensated in cases of lenient exchanges.
Though there are exchange that has a feature of SAFU like Binance which is your fund is safe, still considering it not safe to store your coins there is a long period of time but if you're in trading, I'd like you to choose them than the unknown exchange platform which is commonly considered to be bankrupt due to what you've said.
Some Exchanges may not be trusted as most times they are vulnerable to hacker attackers. Take the case of Bithumb, a South Korean crypto currency exchange that lost a million dollars worth of customers crypto in 2017.
There's nothing you can do if you're a trader, just take a risk, and picking a good exchange was your first step there.
After the trading session just transfers your coin out into your non-custodial wallet, you're safe.
Your privacy matters a lot always use a non-custodial wallet and save yourself the stress.
I tend to agree and you're indeed right.