I don't understand what you're getting at here. Yes, the point of wealth distribution is to reduce income inequality. The UBI achieves that, by taxing high-income people and redistributing it to everyone (in effect redistributing it to the poorer people, because the wealthier people will be paying it all back in taxes). With tax rates fixed, revenue collected will be greater if wealthy peoples' incomes rise, and this will allow the UBI to be indexed up. Why would there be an "upstream battle"? Nothing has to change when the tax rate is the same. What's the problem?