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?

Just as we can still breathe and digest food while sleeping!

We can even adjust our sleeping position while sleeping, possibly to avoid bedsores? But perhaps avoiding falling requires more processing power.