By essential, I don't mean that we depend on it, but that it is evolutionary unavoidable. It may be physically possible for a given process to be performed during wake, yet we are only able to perform it during sleep, because we had already evolved to sleep and thus the process could be optimised in such a way as to become dependent on it.

If we're trying to answer the question of why complex animals evolved to sleep in the first place, then we'd have to find processes which depend inherently on sleep (or at least are enhanced by it).

I agree with your statement - that doesn't mean that there isn't a way around sleep. If we imagine the fitness vs. evolutionary traits as multi-dimensional landscape, it could be that we're stuck on a very deep local minimum. It doesn't mean that there's not a deeper local minimum few blocks away :-)

It just means that sampling evolutionary traits that lead us out of that local minima, is very expensive from a fitness perspective.

> it could be that we're stuck on a very deep local minimum

I think that's likely.

Also, in cases where being able to be awake continually (e.g. high predation or flying over water) animals have evolved unihemispheric sleep, which is likely a shorter evolutionary path and largely satisfies the selective pressure, making it less likely for sleep to be entirely evolved away.