In a live commentary for the film this past Sunday, director Zack Snyder explained the narrative and thematic reasons for why the film ends with Superman's death. Per THR:
Snyder revealed that Superman's death scream, which echoes, was the sound that awakened the Mother Boxes and would have alerted Steppenwolf, hence the Justice League line, "no Kryptonions," which would have also been in Snyder's cut of the film.
The film begins and ends with a death, that of the Waynes, and that of Superman. The canon shot fired at Superman's funeral echoes the bullet firing from Joe Chill's gun at the beginning of the film. Snyder said the cyclical nature of the film was important to him and the death of Thomas and Martha Wayne broke something, while the death of Superman allowed for healing to begin, not only for Bruce Wayne but for humanity. He said that as the film evolved, Superman's sacrifice became more impactful on where the characters were left, citing an earlier idea to have Batman brand Lex at the end of the film, but instead showing him struggle with his rage and refuse to brand him, an initial effort to take Superman's sacrifice to heart.
These ideas make sense, but as I've argued, they leave a Superman-sized hole in the film because we don't know who he is as a character. We understand him as a narrative device (his presence creates escalation) and a thematic device (his death allows for healing to begin), but we don't really know him as an individual. There's really no reason to feel sad when Superman dies other than the feelings you have for the character you bring into the movie rather than anything the film does to pursue your affections. Superman's death has an impact in Batman v Superman, but lacks the emotional punch it needs to really land (especially since the audience knows that Superman will return).