Amusing to imagine the red diesel of sport shooting - better hope the tax authority doesn't find any combustion-proof dye on the self-defense shell casings!
Also brass is often ejected forward of the firing line, meaning cease fire must be called frequently for individuals to collect their brass. And if multiple people are shooting at once, how do they determine who shot which casing? Considering the financial incentives, I could see frequent disagreements over brass ownership.
Then there's the issue of implementation. A proposed law and its implementation are often quite different. For example, California requires a background check when purchasing ammunition. Only California residents can buy ammunition in the state (which creates a problem for out-of-state hunters). This system is plagued with false positives. When I lived in California, I purchased multiple firearms but was unable to buy ammunition due to being incorrectly denied. This happens to 10-16% of legal firearm owners in the state. My assumption is that any sort of ammo tax/refund scheme would be similarly fraught with issues.
Honestly, I think such restrictions are a fool's errand. Both smokeless powder and automatic actions have existed for over a century. Given current US culture, effectively restricting such simple technology would require draconian laws & enforcement of those laws. This is actually a more difficult problem than previous failed attempts to restrict alcohol and other drugs, as the government needs a constant supply of firearms and ammunition.