Storing coins to an exchange "account" (not wallet) for trading is different from making it as an alternative as a wallet. When you see "never store" it is a different way to say, dont send your coins to an exchange.
To store up something basically means to keep in a safe location while you're not actively using it. Day traders are actively trading and as such they are using the funds sent to their wallet, this does not count as storage. Using an exchange account to keep bitcoins you're not using overtime is storing and is not advisable
Exchanges are necessary for trades. Except one has a trusted individual they can trade with, you'll need them.
I have always felt that the exchanger wallet was more secure than my offline wallet.
Note that your offline wallet is the best option, but it puts all the responsibility of safeguarding your address on you. You are responsible for;
• Your private keys (seed phrase) back ups,
• Your choice of wallet software or hardware.
