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).
Hardware wallets can actually function as both. Before the advent of hardware wallets, it made sense to keep a "hot wallet" and a "cold wallet" as you suggest for security purposes. Online PCs/servers can fall prey to malware and attacks in general, and your keys can be stolen. Cold storage and hardware wallets address this.
I haven't gotten one yet personally, so I still use a hot/cold system. I have a small spending wallet on my online PC for convenience and a cold wallet on an air-gapped PC that doesn't connect to the internet. When I need to move coins from cold storage, I create a transaction from a watch-only wallet and sign it from the air-gapped PC.
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?
Hardware wallets are great for UX. They're easy for newbies. Sweeping paper wallets requires setting up cold storage again; hardware wallets can simply be used like a normal wallet.
I also prefer HD seeds to printed private keys because seeds are less obvious to third parties (thieves). You can store a seed in ways that obscure the order of the words (and the existence of the seed itself). They can also theoretically function as a brain wallet.