Because that word lacks any form of punch. Being "privileged" does not imply any personal responsibility; it's essentially saying you got lucky.
My understanding is that this tactic of taking very strong words like "racist" or "nazi" and superextending their definitions is just an attempt to harness the strong emotional response people have to these words and direct it at a very large group of people.
The unfortunate side effect is, that it slowly weakens the terminology, to the point where some day being a "racist" might just not be a big deal anymore.
The more direct danger of this strategy is that, in the short term, while most of the population still associates a term with a different definition, it allows quickly invoking very strong emotions with an accusation that is not technically wrong by the newer definition.
This becomes even more obvious when you look at how people often dance around these definitions to deliberately keep the newer definition as esoteric as possible, so the word retains its connotations for as long as possible.