The idea seems to be that because is descended from Louisoix, the famous Sharlayan hero who saved Eorzea, he's rich.
Rich are often perceived that way, and to be honest, he at first comes across like a privileged person that tries to say he is right and knows best because of where he comes from. Let's be honest, being the rich grandson of Louisoix, the person who destroyed Bahamut, has got to give you an ego trip.
Following in the footsteps of his grandfather, he wants to do great things and the legacy of his grandfather feeds his ego that he can continue it, and he has the perfect solution, a perfect army and the finances to fund it. This feels like a good idea when going through the story.
Obviously, that was naive, because people have their own motivations for doing things and can be corrupt. He learns a lot from the experience, that the world is not so simple.
If you do the coil story, you learn more about his motivations.
Alphinaud tells you this himself multiple times, that what makes him care and everything else is you, and the example that you set, being brave and helping others with problems big and small. He is inspired by that, but before that he was obviously inspired by his grandfather's bravery.
He's a teenager so of course they would underestimate him. Underestimating teenagers is quite normal, even if it's misguided.
He's not seen as the driving force because Minfilia is that, but he does try to fight her for that position for a while until they all realise they don't want or need one. By then Alphinaud has started to realise he had a big ego, and that he needed to get rid of it and be more diplomatic.
