You're just taking a 3 dimensional view of downtown, Mise, which does not bear witness to his full glory. We have to use a 4 dimensional view and a Multiworlds view of downtown to truly understand him.
For instance in your mentioned door case, downtown does leave the door open for his kids in the 4 dimensional view. It's just that in our limited temporal view we have not seen the beautiful children Downtown will sire. But when we talk of what downtown does, we mean it more broadly and in this case his acts as the ultimate father figure.
Similarly we have not seen the full gamut of downtown in other timelines. There are an infinite number of different 4 dimensional downtowns that compose the true downtown we look up to. These different downtowns could be wildly different in setting and career then downtown yet retain the essential downtowness. Astronaut Downtown, Geologist Downtown, Clown Downtown, Lion Tamer Downtown, Bartender Downtown, Grandmother Downtown, the possibilities are endless!
When we speak of "whatever downtown does", we're talking in this meta state not simply the 3 dimensional being that we have the honor to know.