Closed source wallet is not advisable to use because you are not the one in charge of your private keys as it is with the owner of the wallet and at anytime, your wallet can be compromised and you might also be restricted to have access to your funds. This is why you should use a self custody wallet, which only you have your private keys.
The seed phrase is the security of your wallet and that is why you are advice to use a wallet like electrum, bluewallet, unstoppable, passport trezor because you can write down your seed phrase and back it up and store it somewhere no one will have access to but only you, for the proper safety of your coins. Online wallet is only good for keeping small amount of bitcoin for daily spending.
Online wallets are not safe because it is vulnerable to attack by scammers because it is always connected to the internet and there can be a leak, unknown to you. This is why a hardware wallet is recommended because it will never be connected to the internet and the possibility of a hack is very low as long as when you bought it, you scanned through to see that it is safe to use. The safety of any open source wallet is in the hands of the user.