Dishwasher doors aren’t tightly sealed. They are designed to shed water into the washer, like car trunk seals. If you fill them up with suds, the suds will escape (and, if you are unlucky, ruin your controller in the door). Washers are also vented.
I have personal experience that dish soap in the dishwasher creates bubble hell in the kitchen. By personal experience, I mean I did it :o
Cool! As Ruk said, “That was the equation!” Thanks!