To get off the whole bio-media thing and back to your original question about you just having a box with water in it... Well that is a good thing in itself... I am currently building a
sump/refugium for my filtration but lets just say you were to keep the
sump as it is with no bio-media at all. Well it wouldn't be at it's full potential obviously but it would help with at least 4 things.
1. You are basically creating a bigger tank of sorts, simply in two different "buckets". Because they are all interconnected they share the same... well everything. As we all know confining an entire ecosystem to a small capsule versus a 200 gallon tank can be a lot easier for the simple fact that every action (such as fish dying, excrement, excess food,
nitrates, etc..) will have a lot less of an impact on a larger tank. So to break it down in layman's terms.. if you had a fish poo in a 5 gallon it would create a lot more
ammonia ->
nitrite ->
nitrate than if the same fish pooed in a 45 gallon tank. The excess bio-media that you can put in the
sump is just a bonus because it won't fit in the other tank!
2. The tank itself stays topped off more so for aesthetic purposes it doesn't look like your tank is always running low on water.
3. Some people don't want or choose not to have a clean-up crew crowding the tank. I don't know why but they do.. In this scenario you could always put a cleanup crew in the
sump to take care of things if you put sand or if you have algae they might clean the walls as is.. I don't know I always put something in the
sump 
4. A lot easier to distribute chemicals. When putting them in the
sump it filters into the tank a lot slower so it isn't such a shock to the life.
Just my ideas on why a
sump can be very beneficial regardless of what goes in it...
