No one "closes" their system. Of course I can't say it's never been done but water and sewer systems are not hard piped together. Your washing machine has something of an air gap in that the water dumps from the top, but there is also a lid. The lid locks. So your water and sewer are tied together without the standpipe.
By closed I mean no opening, such as what I have now. There is no permanent opening. I can remove a cap off the 4" to make an opening if/when I choose.
While the laundry machine has a water-in and a waste-out port, are they really tied together in the sense that the waste-out can feed into the water-in? That would be a nasty situation. Are you saying that a air-gap drain (flex pipe stuck into a standpipe) is the only thing preventing waste-out from getting into the water-in port?