Aquarium backgrounds are a good idea for more than one reason. One idea behind putting a background in, is to make the fish feel like they are in a more natural environment. They can feel more hidden than being in the front of the tank where it is brighter (less light exposure= more well hidden = less stress). Also it's used as general decor... A background can be prettier than a wall, or the other side of this room you speak of. Fish like to have a place to hide and if you have enough decor and plants (artificial or live), and maybe some that float on the surface as well, you can achieve this for them without background.
Background will also keep from additional natural light from hitting all sides of the tank. The less natural light you have on your aquarium = less algae growth = more oxygen in your tank = healthier environment/less stress on your fish.
Side note: when you bring fish home in a clear bag it's typically recommended to put that bag into a paper or colored bag or bucket to reduce stress during transport. This is the same concept.