Agree on the first point.
I use a flat tax mainly for ease of calculation and demonstration, but there is no reason why this couldn’t be made progressively higher as incomes rise. The principle remains the same.
I would add that the measure of whether tax is progressive, should be made across the whole taxation system. There’s no point making one tax super progressive if other taxes are deeply regressive. The key is to evaluate the whole.
Also, my personal preference would be to tax capital and land more effectively and redistribute the proceeds, thus using that exponential income growth more fairly.