Why birds do not fall while sleeping

This article doesn't even try to address what I feel is the deeper and more interesting question (but probably one that can't be answered): Why is it that horses, cows, giraffes and birds have all had to come up with a purely passive solution of "locking" themselves in place, either via their joints (for the four-legged), or via the tendon mechanism described here for birds?

I.e. why wasn't in simpler in evolutionary terms to come up with some mechanism where 1% of the brain was dedicated to the relatively simple task of "station keeping", while the rest of the brain could benefit from sleep?

Also, why didn't any animal evolve a way to avoid sleep completely?

I thought that dolphins could avoid having to sleep while travelling long distances by having part of the brain asleep and then switching when tired.

I could just be misremembering things, so I’m not certain.