> The problem with (too much) simplification is that it removes political steering capability.
This is not a problem, this is a benefit. If you separate tax collection from tax policy you are still able making economic and social policy via other tools.
Basically tax policy is a low bar to entry way to get the laws you want but in a lossy capacity. Instead of making something legal/illegal outright you can just make it "illegal unless you jump through hoops and/or pay money" or you can provide a tax incentive for something you like (easier to sell than a subsidy). This lets you get dumb policy that would otherwise never pass. Big business benefits from this by getting carve-outs that make them more money or by getting policy that lets them use scale to their advantage. The authoritarian upper middle class benefits from this by using tax policy to create a carrot/stick system to kinda sorta make the poors act the way they want. And of course the government and politicians benefits from the current system because it gives them influence and power.
So right now we've got big business, the top ~30% or so of society and politicians/the government benefiting from the status quo. In order to remove politics from taxes big business is going to have to pay more (or everyone else will have to pay less, an equally large pill for a lot of people to swallow), the upper middle class will have to lose a set of carrots/sticks to kick the poors around and the government will have to accept a net decrease in power. The only way to get these groups to accept this is to spend a century boiling the frog. I don't think we'll ever get simple tax policy overnight.
This is not a problem, this is a benefit. If you separate tax collection from tax policy you are still able making economic and social policy via other tools.