Should a calendar date picker widget show leading zeroes in the selected date and month?

In many -- possibly most -- calendar date picker widgets for U.S. users which display the selected date in month/day/year format, leading zeroes are shown when showing a single-digit month and/or day value. For example, the date March 1, 2018 would be rendered as 03/01/2018.

For example, here's the date picker on the expedia.com homepage (as of Feb 27, 2018):

However, most people (at least in the U.S.) don't actually write dates that way. They omit the leading zeroes, like 3/1/2018.

Is there a good reason that the MM/DD/YYYY format is in such common use in calendar date picker widets? Have there been any usability analyses done that point to one displaying leading zeroes -- or not -- as being superior from a UX perspective?