Efficiency isn’t the issue – far from it, in fact! Electrical neurons work by generating a constant low-level electrical imbalance in their membranes (usually around 40 mV, but that’s not always so), then neutralizing that imbalance in what’s called an “action potential.”
This depolarization cascades down the axon, gets pooped into another neuron by chemicals, and continues until it hits something that can deal with it. Having a brain made out of something that doesn’t slosh or jiggle around would make AP transmission a lot quicker and easier.
No, the big BIG problem with having a rigid brain would be growth and maintenance. Brains are mooshy b/c they’re basically electric fat, made of cells, so growth by cell-division and repair by eating the old stuff and making new stuff is pretty much easycakes McGee. However, when you try to substitute mooshy cellular tissue for something rigid, the energy requirements for growth and the difficulty of eating broken stuff goes crazy.
A good example is bone: bones aren’t made of cells. Rather, they’re made of rubbery connective proteins that are reinforced by metal phosphate struts. Since they need to withstand impact, these struts are very strong, but your bones need whole swarms of acid-belching, metal-phosphate-pooping worker cells to reshape them as you go about life, repair them if they break, and grow more if you’re a kid. The process of bone growth takes ages, and hurts the whole time.
Now imagine doing that, but instead of a simple rod, you’re weaving your rigid structure into an electrically conductive network capable of supporting consciousness and billions of years of redundant junk programming. At that scale and order of structural complexity, the process would take FAR longer than the 9 months it takes a regular person’s brain to grow, upkeep would be a nightmare, and a slight tap to the casing would shatter your brain to pieces – something that a mooshy meat-brain can take with comparatively few ill effects.
tl;dr, meat-brain better than bone-brain for living systems