Already said, but I tend to just disable eggs as cookable (as soon as any type of egg appears, which might mean that a given rare breed might lose the very first clutch to the cooks, before you can make that distinction), as well as making eggs one of the very few things that I exclude from food stockpiles (which can be done for all varieties, right from the get-go).
At least until I have various avian breeds to excess, then I may enable such things to take full advantage of my enlarged population. Although often I still want to ignore eggs as a food-source and instead just butcher the least favourable birds in a move that is part eugenics and part delayed-gratification-meat-production.
The standard answer always seems to be lock them in, but I find that no advantage. (I tend to like plucking young birds from the pasture and get them seconded out to "guard pastures", where they act as lookouts. Always handy to be able to move the brids around and put them in these (and then lock the doors I installed around the guard pastures, so that they don't get scared off-station by one sneaking enemy, and potentially let another sneaking enemy through while someone mobilises to put them back, or get equally scared trying... But that's just the way I work well, YMMV.)