The point of BI is to redistribute consumption to the lower end of the economic distribution, at the expense of the higher end, not to increase overall consumption, though that might happen as a side effect.
The net increase in consumption minus the net productivity gains will be the cost of BI, paid to increase economic equality. However, I have seen quite a few (in fact I would say most) proponents of BI argue that the "cost" will be negative, that the productivity gains will, overall, exceed the increase in consumption.
A basis for this claim is that the marginal return on consumption for poorer people is higher than for richer people, and so they can more efficiently use the redistributed consumption, leading to higher overall productivity. The issue of consumption is, therefore, only half of the argument, and must always be considered in tandem with productivity.
The answer to your final question in this context is that we should favour BI because it is intended to increase net productivity at the same time as increasing consumption on the low end: we will have our cake and eat it.
The issue here is not distribution of wealth, it's consumption. The more we consume now, the less we invest in the future. Do you disagree that BI will increase consumption?
Concretely, we could invest in reducing CO2 emissions, building Tesla factories or developing Tinder for Dogs. Alternatively, we could continue emitting CO2, skip the new Tesla factory and instead just ramp up production in the old Toyota factory, and continue producing goods for poor people to consume.
BI pushes us toward the latter alternative. Why should we favor this?