I see a need for the auto-archive function to have an associated checkbox with it saying "Everywhere?" as it is currently only archiving on the board where the rule is.
Why this, you might think? Well, there's a beautiful scenario where you have a lot of planned cards in your backlog and once a card (which has been worked on in a kanban board), is archived in both places, you can select to still show the archived cards in the backlog making for a very nice and visual confirmation of what has been completed and not. Furthermore, all aggregation columns will be recalculated to not include the archived cards which is a very useful and automated thing. Arguably, sometimes you don't want to exclude the properties and values of archived cards, and so the "Show archived cards" would also have to have a checkbox indicating how to count when showing archived cards.