The protagonist's growth as a hero in "Solo Leveling" significantly impacts the story by driving the narrative forward and creating tension and excitement for the readers. As the protagonist becomes stronger and faces more powerful enemies, it leads to intense battles, character development, and plot progression. Additionally, his growth also affects the relationships with other characters, his motivations, and the overall direction of the story. Overall, the protagonist's growth as a hero is a central element that shapes the story and keeps readers engaged and invested in the series.