Hardware wallets don't work with websites (outside of Trezor's website working with Trezor and Ledger with Ledger) as they aren't to secure your accounts with Crypto.com, Nexo, Coinbase, etc. A hardware wallet stores your crypto keys. This is NOT the crypto itself, so you can use the recovery phase if something happens to the hardware wallet.
It's not going to be as simple as using an exchange, but it's FAR more secure. There's a saying in crypto "not your keys, not your coins" because right now the website has the keys to your crypto and thus could do anything with it. If you hold the keys then you control your crypto. That's what a hardware wallet does, it has nothing to do with securing your coins on an exchange website. These aren't like those two factor keychains with 6 digits that change to give you a new password every 30 seconds; those are for website security.