Well, for one thing, the birds on the video are not hawks, they are vultures [I guess 'paravulturing' doesn't sound as good as 'parahawking'
]. Second, birds of prey can fly for hours and hours and hours without getting tired because the shape of their wings allow them to glide on high currents without a whole lot of effort on their part - parrots wings are different and they hardly ever fly for very long. Third, birds of prey were created to fly at very high altitudes [the record is held by a vulture, as a matter of fact]-parrots are not [even macaws fly barely above the canopy and ekkies not even that high]. Fourth, they bond as deeply as parrots would because they also mate for life.
We often extrapolate information from one species and use it as a base for another but it's one thing when you are doing this in terms of physiological functions and a completely different thing when you are talking about physical characteristics needed for survival that took hundreds of thousands of years to fine-tune. Basically, what I am trying to say is that flight is not the same for all flighted birds and this is why there are all different shapes of wings, different feet, different degrees of vision accuracy, etc. You really cannot compare an Egyptian vulture to a, say, Solomon Island eclectus or a blue and gold macaw - it's like saying that because an Arabian horse can run fast, a cow should be able to do it, too.