There are a lot of good anime about adventurers and their rise. It's thus very surprising to me that there aren't many role-playing games (RPGs) of that kind. 

Some things the game could include:

• RPG character progression with classes (Hellgate: London is a good reference for class list)
• Guild: Pretty much every game about adventures out there lacks good guild quests and mechanics. All we have it's just a side-quest storyline that was made only for show. But there should be the main story, guild ranking, training/rest rooms etc.
• Story: I think the game should be focused on the progression of the character, because that's the point of watching him get stronger with each defeated slime or learned technique, but also a good story with a couple of difficult choices never hurts.
• Open world: Of course, the game should have an open world. It doesn't make sense to make a big empty world, it's better to make a small one, but filled with content, monsters and dungeons.
• Dungeons: I think this facilities should be the hardest in the game. Hardest to locate and hardest to pass. 
• Setting: Although I talked about anime, the game doesn't have to look the same. I would gobble up absolutely any option if all the conditions above were met. I think it should be 3D fantasy dynamic game for the best experience.

These are just some thoughts that have accumulated in my head out of indignation that such a game has not yet been invented. I will be glad to hear your thoughts about this project!