That interpretation is bombastically Freudian, a theme that aptly summarizes 20th century literary criticism. Remember that, due to his impotence, Jake is ultimately protected from being used and thrown away by Brett. The title's symbolism is nuanced and dynamic by design.

After a predictable period of darkness at night, the sun rises and casts light on the changes that occurred during the night. Night is the wartime. Illuminating the darkness reveals emptiness where there had previously been potential. Post-war victory is in name only, as characters descend into various forms of self-destruction following the loss of friends, family, and virtue through years of war. And no matter what chaos befalls humanity, the sun also rises; i.e., the universe is indifferent to us and our emotions and our needs and our wars. The sun also rises despite any event that impacts us. Human meaning is imposed.