I found myself thinking "Do people housetrain parrots?" They must, since they usually don't keep the parrots in a cage. I can't imagine they have parrot poop all over their houses.
They make birdie diapers.
Nibbles is getting one for Christmas.

Oyster shell makes a good grit and is good for egg laying and calcium. Just a sprinkle on the for everyday like salting your food.
Birds who go outside pick up enough sand and dirt for their grit needs.