What I see here is a classic case how most new users of cryptocurrency are thinking when it comes to wallets. It is usually easier to make account on any online service, then to download wallet to PC / smarthphone, especially if the service not request KYC.
Although using exchanges for storing crypto is not smart move, in some cases it can be a much safer solution then using desktop / mobile wallet. We witnessed a huge number of cases where users of one of the most popular desktop wallet (Electrum), lost significant amounts of BTC due fake wallet / phising exploit. In case when user is using only web wallet / exchange, it just need to be careful to always use legit site, and that device is clean from malware / virus threats.
Some small amount of coins can always be stored in exchanges, or desktop / mobile wallet, but whoever has a significant amount of coins should use safer methods, hardware wallets or paper wallets are the only logical choice.
Exchanges usually have big withdrawal fee, so multiple withdrawals may come expensive. Also exchanges get hacked now and then.
Web wallets are also targeted now and then by phishing attacks and some don't allow much (or any) control over the tx fees, leading to other troubles.
That's why I always advise proper wallets for small/usual amounts.
(Yes, for big amounts I agree: if spending then hardware wallet, if just holding paper wallet; these are the easy and normal choices.)
good luck, have fun! 
