Do drawing dimensions have to start from datum?

If the request is coming from whoever will be machining or inspecting the part, I would side with them. They know what they need to see to make sure the part ultimately meets the print.

Also, since your first datum is on the opposing face this implies it is getting machined first, hence why it is a reference datum. The geometry of the face you're making the cut in question (in terms of flatness, parallelism, etc) is not defined (at least not in the image you have shared), so measuring off that surface is less precise than measuring off Datum A.

For inspection purposes it is also much easier to have the distance from 'A' explicitly stated as this is the reference surface for the feature parallelism. I imagine surface 'A' would be on an inspection plate, a CMM or indicator would be set to measure the feature surface depth nominally 10 mm from the reference face and measure parallel. No extra math for them required, less room for error.

Generally if someone in manufacturing with more experience asks for something that doesn't immediately make sense to you and you don't have a strong argument against it, there's probably a good reason for it. Like wearing a mask in public.