As somebody else also stated, computers/laptops/cellphones are not so safe either.
If you know well the person(s) and they trust you, generate for them a paper wallet and ask them to transfer the coins there (maybe even keep yourself a copy for the case they lose theirs!!).
If you are the owner of an exchange and can afford 1 day of downtime... simulate a hack: show temporarily 0 funds to everybody and show a vague info that could be read as "exchange hacked".
Then next day, after you were on the news, you can tell "it was only a drill, don't panic, but please use your own wallets, for more safety".
It could be a good advertising after all
Sure, your computer may not be safe, but you can take responsibility of your own computer. You have options, you have control over it. Now, what control you have over it if you give your private keys to some website? it's just not the same.
If you have an electrum wallet, or a core wallet, you can save several backups, it's impossible that you end up with an empty pocket.