It's often said that Iron Man. The Man of Steel simply doesn't have half the weaknesses that make viewers relate to other superheroes. However, many comic books, animated shows, and TV shows have confirmed that Superman can be an interesting character despite his invincibility.
Thor, a character who doesn't have as many iconic comic book storylines as Superman and only made his cinematic debut in 2011, has thrived in the MCU. Thor started out as an arrogant prince in pursuit of the Asgardian throne. When punished by Odin and banished to Earth, he found love and humility and learned to be worthy of Avengers Endgame due to his characteristic arrogance temporarily ruining the plan.
Thor's constant struggle with his owns selfishness and his inability to adapt to change is what builds his character and it's something that DCEU could learn from when it comes to Superman. This is most evident when Thor chose not to go for Thanos's head in a killshot in Avengers: Infinity War, as limitless amounts of power didn't have a say in his decision to inflict pain on the Mad Titan instead of ending the battle instantly. Similarly, Thor's reluctance to get out of his hut - and his own head - in Avengers: Endgame led him to become "Fat Thor," an alcoholic shut-in who turned a blind eye on his Asgardian potential. It was Thor's inner struggle that forced him to change drastically over the span of seven movies and one cameo. His superpowers never overshadowed his character arc or that of his fellow Avengers, even when he fought side by side with them. In fact, the MCU's careful narrative allowed Thor to fight alongside mortal heroes like Black Widow and Hawkeye with the same dramatic weight, whereas Superman simply swooped in and saved all of his teammates in the theatrical cut of Justice League.
Man of Steel, Superman never truly evolved in the DCEU. Although the scene was controversial, the DCEU made a step in the right direction when Pa Kent refused Clark's help during a tornado. Clark Kent could have been the most powerful being in the universe, but his father knew it was time to go and Clark couldn't do anything about it. Similarly, Superman's last-second decision to kill Zod in order to save innocent lives was also met with controversy, but the moment also set up Superman's inability to avoid death — a moral quandary that can't be fixed with superpowers. Superman's internal conflict had the correct foundations. Unfortunately, it was overshadowed by the relevance his immense power had on the plot of every movie he appeared in.
The last clear hint at Superman's solid character arc is perhaps Superman's helplessness when he couldn't prevent Thor's tragic MCU character arc.