Egg cups are useful if you like dipping strips of toast in soft boiled eggs while the shells are too hot to hold with your fingers.
That's about it.
I remember them from when I was a little kid. Okay, when I was young.
That's a running joke between me and my wife. When she says "when I was little" I just laugh and remind her that she is still little, so she changes it to "when I was young".
And, in my case, I was never little. My mother used to tell me about the funny looks she got when I was a baby and she took me to the changing room at a shopping mall, I was like 12 months but I was as big as a 3 or 4 year old.