Thanks @beanz.
Yeah, Google as well as Dropbox already support these kinds of keys, but I wish they would go further. Google actually only tends to ask me for my key when I am starting to use a new device, but they are convenient enough that I could authenticate much more often. This would mean there's less need to keep your computers fully secure as well.
You can see some companies which support U2F keys already here:
https://www.yubico.com/about/background/fido/