Privilege doesn’t seem like a vague, over-generalized term to me. My dictionary defines it as:

a. A special advantage, immunity, permission, right, or benefit granted to or enjoyed by an individual, class, or caste.

b. Such an advantage, immunity, or right held as a prerogative of status or rank, and exercised to the exclusion or detriment of others. The principle of granting and maintaining a special right or immunity: a society based on privilege.
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