I think certain playstyles do lend themselves towards feelings of 'I'm a big deal' more than others. Characters that affect large areas, that have a stronger effective impact on team decisions or that have really exaggerated high moments tend to deliver on that somewhat. Azir's a really good example. He's generally around the power level of any other champion, but he does capture some of that 'Ruler of a giant empire' feeling in game.
There's certainly going to be some degree of disconnect between status in the world and state in a game of LoL though. To some extent that's just a needed fiction if you want a really varied cast able to fairly compete with each other (e.g. Graves the outlaw with a gun versus Bard the unknowable cosmic caretaker) and gameplay effects that aren't excessively limited (e.g. regular humans not getting killed by a single Caitlyn headshot).