Seems that you have come across one of those weeds that like many greens can be eaten, but they have a fairly specific period when they are not tart. Young leaves are edible but, as they become larger, well as you said, they become bitter.
Good for parrots? Well, that question is likely near to your findings. Because there is a narrow window for the leaf to have reasonable flavor, they likely would avoid them in the wild.
As you know, a plant that develops a bitter taste does so to limit its being eaten. Since this may involve their increasing a toxin contain in the leaf and as you have likely found, there is very little documentation.
I would not target them as a food source. Based on a very limited time that they maybe safe.
