The egg version is to help it hold together a heck of a lot of cheese. The trick is, it can break really easily: if you get it too hot, the eggs curdle. If you want to do this, I'd say keep it in a pot and don't bake it.
KYHeirloomer, I honestly didn't mean to cast aspersions. Nor, in fact, was I the one who asked for explanations. I am not actually a huge fan of most mac-and-cheese, because I think it's usually gluey and doesn't taste much of the cheeses it's made from; I'd rather have something more like a classic Alfredo sauce made properly --- lighter, simpler, and frankly cheesier. If I'm going to eat something like mac-and-cheese, I'd prefer a casserole that had something more in it, in which case what you're looking at is a casserole made from old-fashioned French-style crepe filling but using elbow macaroni as the starch instead of crepes. Tuna casserole, for example, rocks.
I will say that it is remarkably easy to convert children to a simplistic Alfredo-style sauce. You just melt butter, add a little cream and a little grated Parmesan, add the just-boiled noodles with a little of the boiling water, and shake on more grated cheese of whatever kind as you toss. When it smooths out, serve instantly. My son and his pals at nursery school are big fans of this --- which has actually caused some difficulty when other parents find their kids would prefer "Sam's dad's mac and cheese" and ask me which brand I buy, and I have to explain what I've done. They hate that. I've tried pointing out that it's actually faster than most "instant" brands, but they don't really believe me --- perhaps it's not true if the microwave is your principal cooking utensil. But the point is, in my experience what the kids really like is strong, dry cheese flavor with wiggly noodles. Their ideal would be Penne Alfredo --- yes, penne, or some very similar smallish dry noodle with an attractive shape. They want it very cheesy, every kid I know adores real Parmigiano Reggiano, and they want that flavor strongly. Beyond that, I don't find kids are such big fans of goo as all that: they'd rather have a smooth, strongly napping sauce than something sticky.
Of course, since the OP wasn't focused on kids, that's all trivia, but in case someone searches.
In passing, every kid I have ever met loves bacon, so consider using some in producing the fat base.
OK, KYHeirloomer, it's up to you: I want you to try Penne Alfredo, made properly with high-end bacon or cured ham, good Parmesan, and sweet cream. Stir in some fresh peas just before it's done, just to warm them. Now tell me what you think.
As you say, just another pasta dish. But an awfully good one, no?