The way I see it each monster has its role. Godzilla "The Alpha Predator", he seeks and destroys anything that creates this "imbalance" to the nature of things. How long before man becomes the next imbalance.
Mothra "The Deity", Im assuming she is treated like a "God" not because she is a danger to her disciples but to whatever tries to harm her or her people. So shes like super nice to anyone who is peaceful to her.
We need Rodan to be this Rogue monster, he is virtually untouchable. Yes Mothra can fly, but Rodan can fly at speeds of mach one, he doesn't need to hit his opponent or a building to destroy it. So he can do whatever he pleases and just flyaway when outmatched. His place in this band of giants needs to balance the story arch to be interesting. Maybe I like the movie Ghidorah, The 3 Headed Monster so much is because these 3 monsters put aside their differences and fought a bigger threat to the planet. Rodan was this badass! Gave Godzilla a run for his money in that movie. Rodan proved to be a force to be reasoned with. But in that movie we saw into the personalities of each monster. Rodan simply said he doesn't care about mankind and if threatened he would just fly away, showing his rogue attitude towards this plight. Hell even in Destroy All Monsters, after King Ghidorah's defeat we see Rodan flying away immediately after the fight, only to be thwarted by The Kilaaks "Fire Monster". Rodan was alone and flying away. Showing what he felt about joining forces with other monsters. I know it shows Rodan at the ending at the new Monsterland along with all the other monsters, but he wants to be high up in the mountains, away from other kaiju. He likes being alone.
Godzilla and Mothra have a stake in this fight. They both seem to have an agenda to fight Ghidorah for one reason or another. Rodan doesn't give a crap what happens. As long as he survives.
That's my take based on what I understand about Toho Rodan. But Legendary has all the space for whatever Rodan's role will be in this movie.