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They did have official art of eggs that had specific designs in the second gen, so the idea was not spawned by the anime. There has also been merchandise that also had the same designs that were in the anime. I think they have a compendium of egg designs somewhere that they have not shown anyone. It is better for the game to just have one sprite/skin. I will also note that the game does have one unique egg, solely for Manaphy/Phione. It would cost too much memory to have a different design for every base pokemon, and there's also the complication that some pokes have more than one result of breeding depending on whether you used an incense or not, so some evolved pokes have them, too.
Me, bugger this whole thing. I only let the things that should hatch from eggs lay eggs. The rest give live birth, make seeds or spores, or asexually reproduce.
