Any of a kind Bitcoin wallet need to share private key on the internet-connected machine.
Bitcoin client has no responsibility for to keep private key secure. If your's machine connected to the internet, your keys can be hijacked, because your machine can be hacked before you import keys.
The questions is, how to trust any of existing crypto-wallets to store private keys?
P.S. My answer is "no trust" to all of them.
I also wonder about the security of our private key putting it in an online world so it would be possible to the attackers to do anything about it because it is an internet connected machine so it would be always possible to all hackers to do evil things. Unless if we have that kind of security like authenticator that no one can access your credential and good things about its an offline mode.