powdered eggs are readily available and work very well in baking.  I don't know if I would ever consider going to the bother of dehydrating eggs.

We take fresh eggs for the first few days, but if I am going to bake, I usually just mix the powdered eggs in with whatever I plan to bake at home when I am getting my ingredients into a Zip-lock bag.  Then add a bit more liquid when mixing up my batter/dough.

I would not make my own powdered eggs.  Have you tried making cakes, brownies and cookies without the eggs at all?  We cook via an outback oven or nested pans to create an oven and typically will omit the eggs, add a very little more water and oil, and call it good.  I was once told that the eggs used in baking flour products are primarily to keep it together for durations longer than our typical dessert lifetime (a few hours max).  Sure, if I have powdered eggs, I'll add some to the mix, but I wouldn't sweat it.  Many people reduce the oil and use applesauce at home, but I don't want to take applesauce either.  Plus oil is good for lots of stuff.

Solotripper- thanks for the link.

I've had outstanding luck with "Ova-Easy" whole powdered eggs. The product is dead easy to use and for the life of me I can't tell any difference. It comes in a plastic package that can be resealed and unopened will last a long time.
As far as leaving the egg out of some recipes; it was explained to me that most times in cake sorts of mixes there is baking powder that provides a gas to expand the flour into a lighter form but the eggs are needed to denature (cook) and fix the loft in place. You know when you look at an uncooked egg the thing is a slippery slimey thing, but cook it and it becomes more or less firm. Well, imagine the cake batter cooking; as the gas heats and expands at the same time the egg is cooking and as it does it's structure will hold the shape of the gas bubble long after the cake has cooled and the gas is long gone. The other option is to eat your cake in a form something like flat bread, which isn't the worst thing that ever happened in the world.
Just say'n....
Best Wishes, Rob