You don't need to catch them all, just certain ones, but those ones you REALLY need to catch. Or someone else will catch the ones they need and then the game will be over. Plus, think of those poor pokemon, stuck in a maze, all alone. Just dreadful.
It's a good thing this classic game has been adjusted for a younger audience. Running around to catch those animals sounds exhausting, but they'll have the energy for it. Wait, the game is about building the city? Well, that takes a lot of energy too.