You don't need points to take good care of your Tamagotchi. Even with 0 points, your Tamagotchi can live on the meal items and snacks items that are free, like scone, sushi, cone, and pudding.
However, if you want to give your Tamagotchi some more interesting food or snacks, you'll have to buy them, and in order to do that you'll need points.
Also, some of the souvenirs require using points. You have to donate points to the king before you can visit him, and you have to purchase travel tickets before you can travel.
