If hardware wallets became unusable, would confidence in Bitcoin weaken, or would people adapt with new storage methods? Is this even a possibility ?
To make it more simpler for you, let me say it in a lame man language other from what the first reply put it.
Bitcoin are not stored on the wallet we use, they are on the blockchain, our kind of wallet only helps us have access to the locking and unlocking keys to connect to the blockchain where our bitcoin is stored, so in case you have a faulty hardware wallet, just import your wallet on another device and that's all, once you have the necessary unblocking keys to it on blockchain.
Bitcoin survival doesn't depend on any wallets whether cold or hot, it's survival depends on the Blockchain which I believe is very secured, I know that wallet issues regarding Bitcoin are secondary. Your Bitcoin is not stored in your wallet as others have said, the wallet is the access to your Bitcoin that is safe in the Blockchain, that is why we need to priotize the security of our wallets. If you have your seed phrase intact you only need to import your Bitcoin through another wallet and your Bitcoin is still intact in the Blockchain. If the Blockchain were to be compromised that is when we can panic but so far their is no indications of that happening.