2) Having a paper wallet (encrypted with BIP38). The problem: You can easily lose a piece of paper.
Well, you could also make multiple copies of that piece of paper. Unlike cash, your bitcoins can be in multiple places at once, after all. Imagine losing your wallet on the subway, with all your cash in it, but wait! You have a backup at home! And a potential thief who finds the wallet can't access your cash without a password anyways.
But paper wallets, similarly to hardware wallets, are very recognizable objects (and it will be increasingly recognizable overtime), so a thieft will save it just in case, because he knows there's bitcoins in there, he can also force you reveal a password.
With a wallet.dat file you can put it in a generic usb, hide it well, and nobody would know you own BTC. You don't want some thieft to break into your house at night and then he finds out you have a ledger of a paperwallet, because he will beat you up until you say your password. If all they find is some USB it's harder for them to know it's bitcoin related.