If they'd simplify the tax system and make it a basic: "You earn X, pay Y% regardless of income source"
This would lead to situations where someone getting a raise could potentially lose money. It should be first x amount of income is tax free. Next x amount of income is taxed at this higher rate. After that, income between x and y is taxed at this rate. And any income beyond that is taxed at this rate. This is how it currently works, although tons of people don't understand that and are convinced that them getting a small raise will lower their take home income.
But the poor don't want this because the current system makes them pay 0
This could still very easily be implemented. Income $100,000/year, tax rate is 0. Income between $100,000-$149,000 tax rate is 5%, etc...
"But what about deductions for children/mortgage interest/etc?" Also a simple fix, raise the income brackets substantially, so the first $100k or so isn't taxed at all. This would help tons of people struggling currently. Of course there'd still need to be a way to deal with things like capital gains, and I'd also argue that wealth sitting in an account above a ridiculously high limit should also be heavily taxed. But this would likely be far more efficient and fair than the shit show we've currently got ourselves into.
I agree with your other points.
While we're on a pipe dream, throw in a UBI for EVERYONE that isn't subject to tax. Use taxes on AI and automation that's replaced workers to fund that. This would then be able to replace things like welfare and SNAP benefits, greatly reducing the amount of fraud (Not that this is all that huge of a deal now) and overhead that we're currently using to administer the existing programs.