Unilever isn't suing because someone created an egg-free spread they are suing because Hampton's product, due to the labeling, gives a false impression that the product contains eggs.
Actually they can pick one company.......there is no reason why they would have to sue all the companies. But the other companies aren't doing the same thing while they do use the word "mayo" on the front of their packaging makes it clear that they are egg-free products. Also this is likely the first time that Unilever has felt it was worthwhile to pursue legal action.
Consumers shouldn't have to read the ingredients to find out the true nature of a product. What you be okay if the shoe was on the other foot, for example, if some manufacture labeled a product "vegan" yet included eggs in it? But manufactures pay games with the ingredients lists too.