There exists quite a few of vegan egg replacement products already. I've found egg replacement based on lupinus seed flour to be perfectly adequate for baking sponge cake and frying crepes.

The problem is that a replacement product that doesn't contain the identical substance can replace the original only in some recipes. With "vegan products" in general, you'd have to pay more attention when cooking because it will often not cook exactly the same way as the product it imitates.