Shinoda doesn't "act" like he owns LP. The band members put him up to it because he's the guy that always has something when the band runs into a tough place. So the other band members look to him sometimes. He definitely does most of the work, and he puts the most effort into talking to fans.
Besides, have you SEEN the band's music videos? Live proshot videos? Chester's the only face in Shadow of the Day. Camera's always zoom in on his face and rarely do we get Joe Hahn shots.
The fact is: each band member has a different personality, and Chester doesn't play rodeo clown on stage like Mike can. Rob is quiet. You need to let them play to their strengths and leave them to run the band however they want.