I'm not sure you understand....
In this case the weather stripping is a strip around the whole edge of the door, rubberized plastic. It's mean to SEAL, to create that seal when you close the door you compress the edging to create the seal. If the doors don't close under tension they can't seal...
You live in Ohio, you have no idea what winters are like here =) and here is not that far away. A compression seal as I'm talking about is the difference of 50 dollars a year or more on heating costs. 50 dollars a year could add an extra 12 square feet of bench material.