Comment by tialaramex

The choice to have different keys everywhere is key to how the dumbest Security Keys work and thus ensures that two parties who trust "you" don't have (from this at least) a way to correlate your identity.

A single Security Key can authenticate to Facebook as WeedLover420 and then be used to sign into the Google account of the Secretary of the US Marijuana Task Force and even if both Facebook and Google were co-operating in the work there's no way to connect these authentications. Obviously WeedLover420 is more likely to get caught because they used the same IP address to do both things and they stink of weed and they look stoned all the time, but none of those are because of the Security Key, that was locked down good.