I clearly said that some wallets are created to work as hot wallets and that is true.
Only web wallets can not be used offline. Mobile and desktop wallet can still work offline. That is the reason they are called mobile and desktop wallet. If you still any wallet that is a mobile or desktop app and not working offline to generate keys and addresses, it is a web wallet, the close source unrecommended blockchain.com is am example. Blockstream Green, Bluewallet, Electrum and some others are not web wallet and they can be used offline despite being a software (mobile or desktop) wallet.