1) This is an upgrade to the touch sensitive button that's on all YubiKeys today. The reason you have to touch the key is so that if an attacker gains access to your computer with an attached Yubikey, they will not be able to use it (it requires physical presence). Now that touch sensitive button becomes a fingerprint reader, so it can't be activated by just anyone.

2) The computer/OS doesn't have to support anything for this added feature.

Yeah I would like this for a yubikey I leave plugged into a machine, like my desktop at work. That way I don't have to fish the one I carry on my keyring out of my pocket and remember to bring it home.

For cases like this, when people leave their key permanently attached to a device, it would be nice if the device itself had this functionality built in. I mean, the iPhone already has a secure enclave to store this kind of sensitive data.

You mean like the MacBook Pro?

https://support.apple.com/en-us/HT207054

Yes: this is apparently supported by https://github.com/github/SoftU2F — see https://github.com/github/SoftU2F/pull/29#issuecomment-32408... — but the documentation doesn't reflect that yet.