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),
Not necessarily. Look at how small they can be, such as the paper discs inside casascius coins. If it fits on that, can't you write it on the page of a book on your shelf? Books aren't immediately recognizable as money. What about a curtain rod? There's nothing stopping me from turning that into a wallet. Just stick some numbers in there where they can't be seen.
A lot of people make their paper wallets look like money because that's fun to do. It doesn't have to be that way.