From Rocky Point Bird Observatory
The first owl at the Rocky Point station was a total surprise - a Long-eared Owl! In the past several years we have been lucky to catch one during the season, but it is not a given. This owl species is particularly cryptic & not a lot is known about them here in North America. In order to safely band and weigh larger owls, we put them in a wrap which keeps them calm.
Most of my personal animal burritos have been mammals, and it's never worked for me with them other than to keep their movements somewhat more under control.
I have a better understanding of covering a bird's face to calm them, and I can get how removing all that visual stimuli would be advantageous. Birds already have high heart rates and breathing, so minimizing stress in them is very important to keeping them safe. I tend to think of the body wraps as keeping handlers and the birds safe physically rather than mentally. Even big birds are still just birds and are built to be as light as possible, so they injure very easily. The upside to that is when it seems futile to fight, they will freeze and basically just wait out what you are doing. If they fight in a hopeless situation, the probability of injury is just too high, and if they can't fly, they know they will die. So by just letting us do what we want, they will often see being patient as their best outcome, staying chill until they get an opportunity to get away safely, which thankfully we give them once we're done doing whatever procedure to them.
Some will still kick and bite, but once they're wrapped, we know where the danger zones are for our hands. I came across a swaddled Screech owl video with it still putting up its best resistance the other day. While we can't remove their stress or let them know we mean them no harm, we do all that we understand to reduce their stress, as it's important to their health, which is what we are most interested in.
I hope that was somewhat helpful, I'm not the best at bird psychology yet, as most of my hands-on experience is with mammals thus far.