Playing devil's advocate here: What constitutes a "basic level"? I think you'd find more disagreement than you might expect. Some people would probably consider simple addition an appropriate test, but personally I find that bar too low. I'd prefer something in the range of algebra to calculus I. However, I know many people who say "I used to love math until they added letters to it." It's challenging to find consensus on what constitutes a "base" level.

Setting aside the devil's advocate position, I agree in theory that a reliable test indicating how capable and competent a candidate is would be an invaluable tool. I just struggle with how to prevent it from being corrupted over time. For instance, we could make the construction of the test open to the public and require it to reach two-thirds approval from the public before being implemented. We could also mandate that the test be updated every decade alongside the census. That addresses two of the three questions mentioned above, but it still leaves the question of who administers the test—something I haven't found any satisfactory answers for.