The bilirubin in the bile isn't the part that aids in digestion. Bile is a mixture of quite a few things. Some of those things, like bilirubin, are wastes that the body is eliminating in the feces. Other components are functional.

One of the functional components of bile is bile salts. Bile salts are produced in the liver and they aid in digestion by emulsifying fats. Emulsification is important because it makes it easier for the enzymes that digest the fat (lipases from the pancreas, mainly) to access it.

You can live without the spleen because, after its removal, the liver and kidneys will take up its functions.

But the spleen is an important part of the lymphatic and immune system. The same is true for the tonsils and appendix, which are also lymphoid organs that can be safely removed.

It's not dead RBCs that make feces brown. It's a byproduct of hemoglobin catabolism called stercobilin.

Dying RBCs are removed from circulation by the spleen, and the hemoglobin inside them is split into its heme and globin components. The iron is then removed from the heme group. The remainder of the heme is a yellow pigment called bilirubin. Bilirubin is then put into the bloodstream and makes it's way to the liver. Liver cells remove bilirubin from circulation and package it into bile. Bile is released from the liver and gallbladder into the small intestine to aid in the digestion of fats. The bilirubin then works its way through the rest of the GI tract. In the colon, bilirubin is converted by bacteria in other pigments. One of those pigments, stercobilin, is brown.

And that is why feces are brown. It's also why the feces of a person with liver failure or a bile duct obstruction will be gray/white and fatty.

Edit: bike -> bile