Thunder eggs would have to be made more useful for that to make sense (mayo, recipes, crafting...), but if we're going with the Slime Hutch type idea then they could work as is, as long as the chance of getting one was fairly small.
Besides that, stones, ores, and minerals could all be drops, but slimes already do that so it ends up being redundant. If they're hatching into thunderbirds, it could be another alternative to battery crafting, and if a new animal is getting added, at that point I think you might as well add new thunderbird specific drops as well. Maybe feathers?