I was thinking about your comment for a few days now and I realized that the from the natural world, the avocado best fits your Aha! egg substitute fairly well. While in terms of vitamins it won't be the same, but:

1. They look very similar! Both have a large egg/seed in the middle of the white/fruit. Look is important for a substitute, e.g. all of the faux meat products.

2. Nutritionally they're also very similar in terms of fat and protein.