Everybody talks about hardware wallets, but I can't understand what it solves. In my case (and probably for most people), you would want one wallet for "daily" use, and a wallet for long term storage (savings account).

The daily use wallet doesn't require much safety (<$500), so a mobile wallet with the passphrase saved somewhere would work fine.

But what about the "savings account"? It doesn't make much sense for me to buy a hardware wallet? What problem does it solve? As far as I understand I would still need to save the passphrases on a paper anyway (in case of hardware failure), so why can't I just print the private key instead?