I wonder what the energy/evolutionary cost of densely-connected brains is. If it's advantageous, why are crows exceptional?

In terms of why bird brains would be exceptionally efficient for their volume (and I assume by extension, mass), would be that weight is at a premium for them.

Maybe they require the equivalent of advanced EUV machines to make?

It could simply be an evolutionary "discovery", with no particular advantage over our "brain model". Evolution doesn't seek out optima; it simply encourages genetic structures that improve odds of reproductive success.

Or, to put it another way: if corvid genetics happened upon a brain type that promoted their survival, it doesn't matter if it was "better" or "worse" than the path the monkey/hominid brains took. Genetics took the first bus going in that direction.