Sure. I guess I was pointing out in a roundabout way that one of the assumptions must be wrong. I don't think 2,300/hr feels realistic. 200 seems much more reasonable (or less). I'd be inclined to believe 1 nail per minute (sustained). If you assume $20-40/hr, now we're up $2-4/nail which seems much more reasonable.
I can't find the price of nails in roman times, but 300 years ago it was around a buck a nail.
https://www.nber.org/digest/202203/tracking-price-nails-1695