TBD, I understand what you're saying regarding the reasons for using using "inventory" as a verb as opposed to "search", however, the term "inventory search" is used by the Supreme Court justices in their decisions affirming the authority of the police to do "inventory searches" in many cases, so I think it's not a big deal if a cop said he conducted an "inventory search" as opposed to an "inventory" of an impounded vehicle: Colorado v. Bertine (full text) :: 479 U.S. 367 (1987) :: Justia U.S. Supreme Court Center