They can... but I mean, it's much like Animal Crossing though - you set what it is you want to achieve as your personal goal. You don't have to catch every bug or fish or pay off your house or participate in the extra fancy house judging or catalog everything in the game. But it's there if you want to.
Pokémon is the same way for me. I really don't need to catch them all, and I don't need to level them to 100, I don't need to complete all the gyms or beat the Elite Four. I pick and choose the things I want to do. For me, I'm happy collecting the cute pokémon I want, leveling them enough to beat the E4, and then I'm good. All the "end game" stuff I could go back and do but I don't really get into it THAT much. But I do enjoy the time I spend in there and still consider myself part of that community.