Not as simple as it may first appear. If the skis are not pointing in the same direction as the CoM is moving when the are engaged, you also lose energy due to the "impact". It does not matter if the turn is carved or not. Since the skis and CoM trade places during transition, this direction difference will always happen.If you are carving arc-2-arc you are losing the minimum amount of energy to friction and doing the least amount of work on the moving object to slow it down. A force applied at 90 degrees to the moving object does not slow it down, only the friction force applied tangentially to it slows it down.
With no losses, all of the potential energy due to height, mgh becomes kinetic energy, 1/2 m (V^2), your velocity would be the square root of 2gh after desending a height of h. A little less with losses IFF you are pure arc-2-arc carving. You will quickly reach terminal velocity on steeps if you are pure arc-2-arc carving.
If you do not have a DH or SG ski with a LOOOOONG turn radius, you will not be carving pure arc-2-arc turns at the speeds you will soon reach on steeps with good carving technique.
It's simple physics:
To hold a 2 g turn with a 26 m turn radius ski you need to tip it up to 63 degrees to reach critical angle. Tipping that 26 m ski up that far reduces your turn radius to about 12 m. A 12 m turn at 2 gs will give you a speed of 55 kph. Far above the speed you would reach on steeps with good carving. This applies roughly to a hard surface. You can feel the difference if you go out and make some turns back to back with an old SG ski and any modern shapely ski.
Also. the 2g/63 degree only holds if you assume static balance. In a good turn the upwards acceleration may be around 2g as well.
It is like if a magic force is pushing your skis down into the snow with a force corresponding to twice your weight. 63 degrees on top of that and you have some serious edge hold. Static, i.e. no upwards acceleration, you are doomed.
55 is not that fast is it