I personally don’t feel the need for a funeral or anything after I die. However, I don’t think funerals etc. are for the dead. They are for the living. So whether it is the right thing or not should be something the family have some input into. If they are okay with no formal occasion to see the person off, then it would be fine.
I think you do have to think about it carefully though. I have said here before my mother died when I was a child and my father didn’t believe in having any markers. When I was an adult and getting married, I really, really wanted to take my flowers to wherever my mother was finally laid to rest (she was cremated so I was looking for some sort of marker). There was nothing and I felt a profound sense of loss that there was nothing to show she was ever here. I am a very practical, down-to-earth person and had you asked me before this occasion, I would have agreed with my dad’s stance. Now, I am not so sure. When he died, I was in Australia, but I planted him a tree and every now and then I go to the house where I lived then and look at that tree. It is comforting somehow. Just some thoughts.