What I'm proposing is that the electrical box (the blue plastic thing that's essentially non-removable in current practice) would have the vampire connection to one or more cables passing into/through it, and the actual device (outlet, switch, light fixture) would plug into some conductors at the back of the box. So you could replace outlets more easily than you can today.

The boxes would come in a few varieties based on the number of cables that could pass into/through them. Again I'm picturing some kind of intermediate layer between the box and the device that could accommodate less-common connection arrangements, but maybe you lose a bit of flexibility in the name of progress.

The connections wouldn't have to be 100% reliable, but at least as reliable than hand-twisted wires and wire nuts (also AFCI breakers could eliminate a lot of the fire risk).