Basic income does seem to work as a solution to this; also gets rid of the need for minimum wage statutes. Any other schemes?
The main problem with your scheme is that in the far future, free trade could mean that countries with only labor and no capital would get a bad deal, and that without restrictions on people taking their wealth to other countries, the rich could theoretically use this to bargain the tax rate down so low that there was no money for a basic income (i.e. a "race to the bottom"). I don't think this will be an issue for a long time though.
Ideally, the level will be set to what will produce the best outcome based on our current understanding of the world, where the precise parameters under which 'best' is determined is negotiated through a fair political and/or economic process.
In practice, the question is how we best approximate that. The shape of that should be informed by economics, and will likely depend on the particular country.
All of that said, I agree it's a key factor to look at when assessing a particular BI proposal; I don't think it's an unanswerable question.
But why? Income tax is supposed to support the infrastructure needed to maintain and protect all of our great stuff. The fact that robots did all the work doesn't negate the need for roads and wars and bank bailouts. I wonder, if we still had slavery, would slave owners be required to pay income tax for the income generated by their slaves?