Handwritten paperwallet or hardwarewallet to store Bitcoins?
True.
There is a standard algorithm for generating the keys from the seed words (BIP 39 / BIP 32).  Most hardware wallets follow this algorithm (check before you buy).  So even if the hardware device has failed or cannot be used, you can still use your written seed words with any other software or hardware device that implements the standard algorithm to recover your keys and spend your coins.
True.
True.  But if you are paranoid, you could generate your own seed words with some more trusted software, import them into your wallet, and check with some other software that the hardware wallet is correctly generating the keys from them.  That would guarantee that the keys are secure, though of course it wouldn't rule out the possibility that the hardware wallet is secretly sending them back to the manufacturer or another attacker.