In nature most of the cells are mononucleated, but in some cases like osteoclasts, umbrella cells of transitional epithelium, tapetal cells of another etc. are multinucleated. Wikipedia article about tapetum says that it is a strategy to increase the production of proteins. Why don't cells just up-regulate their genes for more production? What is the benefit of not having cytokinesis?
The absence of cytokinesis allows the two nuclei to remain in the same cell. If a cell has 2 nuclei instead of 1, it can transcribe DNA to mRNA at double the maximum speed, and so produce the desired proteins at double the rate. It's almost as if the cells become tetraploid, or hexaploid, and so on.
Why is it more desirable to have 1 cell with 2 nuclei than actually do cytokinesis and have 2 cells with 1 nucleus each (still 2 total)?
Because it is unfavorable to create two cells, which needs an extra investment in energy and nutrients to maintain, and is also harder to coordinate, and so it becomes more desirable to just have one single cell with the capacity of producing double the proteins.
Then why don't all cells adopt this strategy? What is the reason for such partiality?
First, because most cells don't need the extra transcription speed, as they don't produce a lot of proteins. Second, because of cell differentiation - to have cells doing different things they have to transcribe their genetic material differently, and so must be separate. Third, a lot of times it is desirable to have extra cells. For example, skin epithelial cells: their main purpose is to serve as a barrier or protection, and so there has to be a lot of them. That's why the basal cells are in constant mitosis.