I know you’re joking, but possible causal path here:
People with Alzheimer’s lose ability to use stove -> eat simpler less involved breakfasts -> eats less eggs
You can, but people don't as a general rule. It's a traditional food prepared traditionally. And importantly, another thing early Alzheimers cases don't do is learn new cooking hacks.
Works surprisingly good indeed. Just get a bowl, stir some eggs, add seasonings of choice and pop it in. Be sure to stop the microwave on time, because the mixture expands a lot.