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.

It literally does, this is one of defining differences of a federal system, that the states have a right to set and collect taxes.

It sorta does, that's one of the primary points of a federal system.

By definition, a federal system does prevent a single point of collection and distribution. If states could not or did not collect taxes on their own authority, it would not be a federal system. States would just be adjuncts of a national government.

You’re absolutely correct. For income taxes many states and the federal government offset each others debts.

In Canada provinces can choose to harmonize taxes or collect independently.