>Right, but engine braking reduces the excess energy leftover once the tires would start skidding,

Again, it doesn't. Think about where the energy for revving up your engine comes from when you're engine braking... It's the wheels rotating against the road, which via the driveshafts make the gears in your gearbox rotate, which via the clutch will turn your engine over.

If you have a motorbike, you can try this out relatively easily - apply rear brake until just before you lock the rear wheel, and then downshift. You'll see that your rear wheel will lock. It has happened to me.