Is there any advantage of filleting a fish at home instead of buying a fillet?
When you cut any food you expose the cut surface to oxygen, which causes chemical changes due to oxidation. You also expose the cut surface to microbes and organisms which break down food. Both of these will impact the quality of cut meat or fish, so yes a filet cut from a whole fish just before cooking would be fresher and better quality than one cut some time before. 

The effect is not great, however. If you had a whole fish and cut one filet from it the day before, then cut the other filet just before cooking both identically I doubt you would be able to tell any difference between the two. 

To me the reasons for buying a whole fish as opposed to filets is cost and choice. A whole fish is easier to judge for quality than a filet, you can see whether the eyes are cloudy or clear, for instance. Buying a whole fish is cheaper than buying the filets off of it because it's much less work for the seller, so you can save some cash doing it yourself. 

However, fileting a fish is not that easy. It's perfectly do-able at home and there's loads of how-to videos but it's still pretty involved and hard to do that well without lots of practice. It's also messy time consuming, so when you buy filets it's for the convenience of not having to do it yourself. The important thing is to make sure it's fresh whether it's whole or already prepped.