While some vegetarians eschew only red meat, pescavores eat only fish as sources of animal protein, and vegans avoid all animal-sourced foods, the newly-recognized group of veggans are basically vegans who eat eggs.
Is this a good trend, health-wise? Probably it is especially for parents who want to raise kids without foods from animal sources, meaning: milk, meat, poultry or fish. It's good because eggs are sources of high-quality protein, iron, as well as vitamins D and B12 (as ACSH pointed out many years ago).
In addition, they provide little in the way of saturated fats, and are actually rather low in calories a large egg adds only 70 or 80 calories to the diet. For growing children, such a source of these essential nutrients has to be a major plus (although the kids may still need to supplement some of them so check with the pediatrician).
While it's true that egg yolks provide around 230 milligrams of cholesterol each, this fact is not as scary as it used to be. We've seen recent research telling us that dietary cholesterol is not the main culprit in causing high blood levels of cholesterol blame that on your liver. Further, someone who follows a nearly vegan diet isn't going to have any other sources of dietary cholesterol it's strictly an animal product. Even the 2015-2020 Dietary Guidelines no longer try to scare consumers away from eggs and dietary cholesterol.
So for those who want a vegan-type lifestyle, but need a more nutrient-rich choice, vegganism may be just the ticket.