It is undisputed that a mile (measure of distance) comes from the latin mille passus. Mille means one thousand (1,000) and passus is translated to the Engish cognate "paces". It is therefore meant to mean "a thousand paces".
This is what we find almost anywhere, e.g. Merriam-Webster:
Middle English, from Old English mīl, from Latin milia miles, from milia passuum,literally, thousands of paces, from milia,plural of mille thousand
First Known Use: before 12th century
A thousands paces cannot cover the distane of 1 mile (1609.34 meter).
The MW definition of a pace:
any of various units of distance based on the length of a human step
Taking into a account differences in body height between now and when the term originated, this makes even less sense.
In sticking with the antropocentric units, I would say that a step is at its greatest length equal to a yard. However, there are 1,760 yards in a mile (admittedly a contemporary convention).
Why does mile/mille passus refer to a distance that is much greater than the distance 1,000 paces can mean?
N.B.: I researched this topic on this website here and elsewhere, and it just states 1,000 paces everywhere.