Nice letter. I think you cover all the points without getting them angry. Nice job.
I think you're definitely correct in both your assumptions and interpretations. Airguns are "outlawed" for hunting purposes mainly to prevent the small proportion of idiots who would have otherwise gone into the woods with their Red Ryder to go coon hunting (or something of bigger size than a sparrow). All the Red Ryder would do is hurt the animal and lead to suffering. Rather than putting in language into the law that says "only air rifles with greater than 25 fpe can be used" it's best to outlaw them altogether. There would be too much room for interpretation and selective enforcement otherwise. Just like many states say you must use centerfire only to hunt. Sure, a good rimfire can drop many small animals, but rather than leaving any room for negotiation, they just banned all small calibers.
Remember, laws are always written with the lowest common denominator in mind: the complete idiot. Most hunters are intelligent, know their weapons, and know their animals. Most would never try to use a Red Ryder to shoot a bobcat. But there's the one idiot who would, so laws need to be made. Is it fair? Well, that's for another conversation.