This feature is not p2w.
To keep it short and simple, I think the ability to earn badges, and receiving a reward after earning each badge, would be good for the game.
It would be good for the game because it would encourage people to explore all aspects of the game.
This type of mechanic is typical for MMORPGs.
What type of achievement would you want added to the game? What type of rewards would you like to receive for completing this achievement?