I think there is something conceptually very wrong with that approach. Let me use an example to try to explain why.

I think this is how economists normally think about it, though I am not 100% sure about that.

The normal way to approach that question is to multiply $10,000 by the population, then subtract the cost of Social Assistance (welfare) that would be eliminated, to get the net cost of implementing Basic Income. Then talk about what increase in tax rates would be needed to fund that net cost. [Do not fuss about picky details like adults vs kids, and other programs that might be eliminated, because that is not what this post is about.]

Q. How much would it cost to implement a Basic Income, where everyone gets (say) $10,000 per year?

Micro public finance is not my area, so take this post with a big heap of salt. But:

Suppose under the current system an individual with zero income gets $10,000 in social assistance. And suppose that there is a clawback rate of 50% on any income earned by someone on social assistance, so someone earning $20,000 would get no welfare at all. And suppose that there is a personal exemption so that the first $20,000 of income is tax free, but that any income earned above $20,000 is taxed at 50%.

Now consider scrapping the current system, and replacing it with a $10,000 basic income given to everyone, and a 50% tax rate on all (earned) income starting at zero (the $20,000 personal exemption is eliminated).

By construction, those two tax/transfer systems are identical. Every individual pays exactly the same taxes net of transfer payments under both systems. It costs nothing to replace the existing system with the proposed new system with basic income for everyone. The only thing that has changed is what we name things.

But let's do the costing the normal way, to see what we get.

For simplicity, assume a uniform distribution of incomes from $0 to $40,000. (That makes it self-funding). And let the population be one million.

The cost of giving one million individuals $10,000 will be $10 billion.

Half the population (0.5 million) will be getting social assistance under the current system, and on average they will be getting $5,000 after clawback. So the cost of social assistance is $2.5 billion.

Subtracting the $2.5 billion saved from eliminating social assistance from the $10 billion cost of giving everyone basic income gives us a net cost of $7.5 billion of the new system.

That makes it sound like we have to increase taxes by $7,500 per person on average to switch from the current system to basic income. But we don't. By construction, every individual pays exactly the same amount of taxes net of transfer payments under both systems.

Or you could think about it like this: clawback of social assistance is a tax; and the $20,000 personal exemption is a form of assistance for lower income individuals that can be replaced by basic income.

This is an argument in support of basic income. But it is also an argument against basic income. There are no costs to implementing basic income as proposed here. But neither are there any benefits. It's just a new name for the old system. It's not a magic wand.

Any benefits from basic income must come from: reducing administrative costs and busybodyness; and smoothing out the rat's nest of bizarre spiky marginal net tax rates under the actual existing current system.