Is it possible to make a part that meets the requirements? Yes.
Do large variations in the datum features make that more difficult? Maybe.
Do large variations mean the inspector might have to do some work to fit the feature to the tolerance zone? That's the thing that's being complained about.
They can't just slap the part onto the CMM, click their heels three times, and be done. They might have to shim the part, maintaining contact with the datum feature simulator per the ASME Y14.5.1 requirements and they don't want to do that.
Now, if datum feature A is a 1000 mm diameter flat and the thickness of the part is 0.0001 mm, how much rocking of the part will there be that they are worried might happen?
Knowing only the zone and not the actual sizes of the part means not being able to calculate for you the amount of rocking that might occur.
It also means that if datum feature A is 0.01 mm diameter flat and the part is 20 meters long, then rocking might be a huge problem. But no information means no applicable answer.
Which is why all the dimensions are important and not just the allowable tolerances which, by themselves, are nearly meaningless in making a decision.