Because storing encrypted online is both harder to do right and if your computer has malware on it then no amount of encryption will save you because at some point you will need to decrypt your keys. Not to mention that someone can still try to guess your encryption phrase.
With a hardware wallet your private keys never touch your computer so they can't be stolen. Even if you are the kind of person that can't resist clicking on every piece of malware you encounter your Bitcoins can't be stolen from a hardware wallet.
Bottom line hardware wallets are easy to get right.
A hardware wallet allows you to spend coins without exposing the private keys. To spend e.g. a paper wallet, you have to swipe the keys on a computer. Yes, that can be offline, but a HW wallet reduces the amount of possible mistakes in this process.
Speaking of Trezor: "a recovery seed is generated when the device is initialized. In case TREZOR gets lost or stolen, all its contents can be recovered using this seed (private keys, bitcoin balance and transaction history) into a new device or another BIP 0039/BIP 0044 compatible wallet." [1]
See also the "Security threats" chapter from the official documentation. [2]
Yes, in the case of the Ledger Nano S for example when you set it up for the first time it gives you a 24 word recovery seed that you write down and keep in the safe place. The seed is created according to a Bitcoin standard (BIP39) If anything happens to your hardware wallet you just buy a new hardware wallet that supports BIP39 and you are back in business.
If you want to be really secure you can engrave your recovery seed into a piece of metal that won't melt in typical house fire temps like brass.
Thanks for the detailed answer, exactly what I needed! Would you recommend the Ledger Nano S? It seems like it's half the price of Trezor for some reason.
I have a nano, it does the job. Build quality feels cheap but like you said it is half the cost of trezor. Keep key is a trezor clone trezor was first in the space and I think there build quality is better
Ledger Nano s, Trezor, and KeepKey all stop this sort of attack.