I'd be more inclined to suggest egg based foods are going to be CCPs but with baked products, the rule of thumb I always had was that if the point you needed to cook it to for food safety was close to the point where it would be acceptable for quality, it's probably a CCP. For bread for example, you'd still have dough when you're well past the food safety limit.
For egg based products, I suggest those temperatures are pretty close.
There is a famous controversy in Spain about their tortillas (not the bread, the egg based potato omelette) and how the traditional way of cooking them perhaps caused a food safety incident.
How to cook Spanish tortilla: Salmonella outbreak sparks national debate - BBC News
Some people will not reject egg products that are perhaps a little underdone. Especially if they come from countries with vaccinated flocks. Runny yolks in the UK are commonly eaten but when they're shown on Facebook recipe videos, the US posters are up in arms "needs more cooking!"
(From the country that eats rare hamburgers... But that's another topic!)
