It seems efficient and simple that way. But you don't want federal politics playing that much of a part of your local life. And you don't want your local politicians to have to pander to the federal levels just to get what they need or what is theirs. I think this would result in disaster as the federal politicians are too out of touch with local needs.

If we had a single formula for taxes, then each taxing body could have their own rate table to apply to it, but still collect it directly - then I think that would be a better approach.

For simplicity sake, take income tax at flat rates. Federal may be 20%, your state might be 10%, city might be 5%. Maybe my state rate is only 5% and you might want to move here, but nationally we all pay the Federal 20% rate.