This is a common question and for many years I have said that everyone should use one. I have since changed my mind. I still see the value the in them and still recommend them but now there are conditions.
The reason you use an eye cream is to hydrate the eye area to help with dark circles, puffiness and/or fine lines. This is either a preventative or corrective. The eye area is 7x thinner than your face so it does require something different than your moisturizer so there is definitely a benefit to an eye cream.
I stopped recommending them to everyone because if you are using serums in your routine then I don’t think you need another products for your eyes. Of course, this only applies if you are using the correct serums but I make sure that my clients are using the right ones so they aren’t missing out on anything.
The ingredients in the serums are small enough to penetrate into the eye area and give you what you need. I don’t know why an additional cream/serum is needed. I used myself as the guinea pig for this experiment. I stopped using an eye cream to see if I would see a difference and I haven’t. The serums I use are hydrating and will help with fine lines.
Now, if you aren’t using serums (or the right ones) then you MUST wear an eye cream/serum. Your eyes age the fastest and are the most abused so protect the area now! I suggest people start as young as 18-20.