I think the limit you defined as "if the total level of consumption exceeds the level of production" is really the key to the whole discussion.

If we are in a society where there is no surplus, then having a basic income is not possible. In a theoretical society where there was unlimited resources and robots to provide anything of value, then there would be no need for a basic income because everybody's wants and needs would be met.

So in a way, the purpose of basic income is to divide up the surplus 'fairly' and to some extent equally when society is in a state where there is a large enough surplus to cover everyone's basic needs, but not enough to cover all of society's wants.

There is also the point you touched on, which is that once the requirement to work in order to meet basic needs goes away, there will most likely be a drop in the surplus, because many people would prefer not to work.

While it disproportionately benefits 'rich' people, the stock/equity market actually has some similarities to what you describe, in that people are purchasing ownership in production robots (companies) that provide a share of the production profits to their owners. I'm curious if the expanded ownership of companies through stock ownership has the potential to serve as a vehicle for moving our current society more in that direction.