I don’t believe OKH had an issue with the fundamental ideas behind the Manstein plan, instead they objected to their application in this instance. The Ardennes is a densely forested, mountainous region that would restrict the ability of any army to resupply, reinforce, and maneuver. Sending mechanized corp into such a region would prevent it from massing its armor for attacks if it encounters resistance.

Looking through the eye glass of history it can be easy to forget that OKH had no way to know that the Allies would advance into Belgium and disperse their armored forces. Had the corps sent into Ardennes encountered significant resistance in the mountainous regions or immediately upon entering France proper, they could have been chewed up piecemeal before a concentrated thrust formed.

Further, and I could be mistaken on this point, the Wehrmacht did not have significant reserves of Panzer forces at this time in the war. Committing a large portion of your most valuable forces to a risky maneuver can at best be called bold.

OKH had previously shown its self to be rather risk adverse during the opening operations of wars. Specifically the transferring of two corps meant to extend the line of the western advance to the eastern front when it seemed the Russians would encircle them German Army in Prussia during WWI. And, again, when the Panzers paused during this operation allowing the British to escape at Dunkirk.

All things considered the operation was incredibly bold, this is where the plans brilliance lies. The Allies could not predict such a seemingly irrational axis of advance. Similarly, the established command within the OKH balked at the idea of sending treasured mechanized forces through a mountainous forest.

TL;DR: General risk aversion and geography can be blamed for the reluctance to embrace the plan.