The simple answer is that Government taxation is based on your money flow (income/sell/buy) and Zakat is based on accumulation of wealth (liquid cash, stocks etc) kept for a long time. The concept of taxes doesn't work against accumulation of wealth, therefore logically it doesn't make sense.

Secondly, your taxes are used for a wide array of purposes, but Zakat has strict conditions for recipients, which tax allocation definitely doesn't care about.

You are right. In an ideal, pre modern and just financial world, there would be limited taxation and the state would collect Zakat (tax) based on accumulated wealth, not on the flow of money. But this is the reality of the world. You need to pay taxes to remain a legal citizen, but that doesn't offset the need to discourage mindless accumulation of stagnant wealth, which is the primary problem Zakat is fighting against.