Board Game Arena

Had a co-op mission (5 player) and there were 2 separate missions - each for a character to take an egg.

See I would have played that a single character could take 2 eggs to achieve the missions - but the game ended in a failure [only] because of this (we used duct tape to carry the 2 eggs).

Yeah not a bug. You might be confusing it with the semi coop mission task Primary Sample:
All Characters who Escape from the Facility must be carrying at least 2 Eggs in total among them (no matter if they Survive after Escaping).

The coop mission task is Culinary Sample:
A Character must Escape from the Facility carrying an Egg from the Nest (Section C).

Since you have 2 Culinary Sample missions, you need two people each carrying an egg.

That's working as intended. I think it's covered in the FAQ. If you have multiple missions with the same goal, you can't just have 1 character fulfill it for both.
Your mission states, that a character needs to escape with an egg. To fulfill it twice, 2 characters need not escape with an egg each.