I don't think there ever was a serious risk for that for WhatsApp: multi-device support isn't just missing, they are actively making it a pain. There's no way to obtain your password, the password changes regularily, logging in with a second client kicks the old connection, etc.

So people would be forced to make a choice: use it on your phone, or on your computer. Aside from the group of people who don't have a smartphone, most people would chose phone.