Is he doing this in V/s?
For a given IAS you actually achieve a better TAS at higher altitude. If he is deliberatley climing slower, but is NOT maintaining full climb thrust, he is actually going to take longer to get where he is going.
You could tell him that if he REALLY wants to go fast, maintaining the altitude at which 320IAS is equal to cruise MACH (?.80? in a 320?) will give him the best TAS, but will use a shed load of fuel. Is he willing to justify this?
Bottom line would be, what are your company SOPs?