User Problem

If you want the export to have archived cards, you need to remove the ?cards=visible parameter from the export URL, for example:

This link does not include archived cards - https://trello.com/b/wlgFnMID.csv?cards=visible

This link includes - https://trello.com/b/wlgFnMID.csv

Article for reference.

Suggested Solutions

A more friendly option, such as a checkbox to include the archived cards or a second option "Export CSV with archived cards"

Current Workarounds

Edit the board URL and add .csv at the end. It should look like this: https://trello.com/b/BOARD_ID.csv