I've never heard of a payer asking for CPT/HCPCS codes on an itemized statement, but I don't know of any rule that says they can't ask for it. However, I think it's an unreasonable request and I wouldn't do it for them. An itemized statement of an inpatient claim can contain literally hundreds of items, and for many of which there aren't any specific CPT codes. It would be a nightmare to try to go through all of that and add codes, and I can't imagine that it would be useful to the payer anyway.
There is one situation I can think of where a payer may want to process an inpatient claim as an outpatient claim (for example, if a patient who has part A or part B only and the payer needs to see what the outpatient portion of the services looks like separated from the inpatient room charges). That's a little different, and in that situation, they may want to see a coded outpatient claim for those same services or might request an itemized statement in order to try to make that determination. But that's not what you're describing here as putting CPT/HCPCS codes on an itemized statement, which is something I've not heard of.