Because in this case, it’s a historical drama made for a Korean audience.

When a television show is made, they need to consider things like ratings and ad sales. The series you’re asking about concerns one of the greatest heroes in Korean history. If the studio wants to make money with their product, it serves them to lionize the man and build up his achievements. The arrow shot to the eye you mentioned is a great example - it’s something that probably didn’t happen, but makes for great television (though something similar did happen in English history, which is where the producers may have taken inspiration from).

Exaggerating his history and accomplishments are just par for the course with any sort of drama of this nature. People watch these shows for action, excitement, and to take pride in their nation - not historical accuracy. That’s what documentaries are for.