Clarification:

The problem likely arises from the fact that translateable pages
only exist once for all languages. The defining page contains invariant parts
plus a set of transcluded parts, each of which is translated individually and
independently. Ony at transclusion time, a distinction is made as to which translated language the transcluded parts are taken from, at least as to my
understanding.

The date/time of last modification is taken from the single defining page.
Thus it is independent of the actual translation and independant of
the language that users actually read, and independent of when each
translation was made, although they usally are not made at the same times.

It would be more user friendly to display the most recent of the modification
date/times of the transcluded pieces of a translation since these pertain to
the text that the users read,

Alternatively, one could think about a message of the kind:

"The (language) original of this page was last modifies at (date/time) and its (language) translation at (date/time)"

MediaWiki shows be default when the page is last modified. Last modification on translation pages cannot be anything else but 1) translation update 2) the page template update (=invariant parts of the page).

Isn't this what the users want to see?