>Engine breaking transfers the energy of you moving into engine rotations instead of via the wheels to the road

This is the part you're getting wrong. When you're engine braking, you're still using the friction between the wheels and the road to transfer kinetic energy - only into the engine instead of the brake discs.

The wheels and road play the same role in both cases - the road is your frame of reference for how much kinetic energy you need to shed, and the wheels are your contact point with it. So in both cases, the friction between wheels and road is the initial limiting factor. And if you can break that limit with your brakes alone, there's no use for any engine braking.