Stannis would be a great leader if not for Melisandre. The North (who worship the old gods) would never worship R'hllor, which would lead to Melisandre burning the non believers alive, thus there would be constant rebellion in the North as well as the Iron Isles who also hold a certain devotion to the drowned god. The other realms don't seem as dogmatic
From my understanding, people didn't want Stannis to be king long before Melissandre arrived because Stannis was a little too just. He chopped the fingers off a man who saved his life. I think that's why Renly and some others tried to be king after Robert died. I don't think they knew the extent of Melissandre and the Lord of Light. I think they just didn't think Stannis would be a good king. But I do agree, I think he seems like a just man. To be honest, I thought everyone seemed like a good leader besides the psycho Joffrey.
Renly seemed progessive, Robert had a good heart but lost his passion, Stannis was just but a bit rough, Ned was just and more kind hearted, Tommen seems nice but is young and easily manipulated, Tywin knew how to handle business and politics, Rob (Ned's son) was a fierce leader and strong motivator, Tyrion knew how to handle people and showed good leadership.
I guess that's why it's the Game of Thrones. You have to know how to play.