One deletion can serve two aims: the utterance becomes shorter, and it may avoid restricting the action to a particular recipient. These effects can coincide in the context of a general invitation, but they are not the same meaning.
Economy concerns how much is said; generality concerns the scope of the assertion. An economical sentence may still be about a known specific object, and an overtly expansive sentence may state generality explicitly.
Therefore a combined reading must be justified by context, not by the bare fact of ellipsis.