If I died before my Dad, I think he would want a funeral for closure. They're more for the people left behind- in my view.
I sometimes get the impression people who don't want them feel (most likely, justifiably) that they don't want to give those left behind the chance to fake being upset and to make it all about them. That's the impression I sometimes get.
In my case, my Dad is the last remaining close family member I still have alive. But- I don't intend to CTB till after he goes. After that, my intention is to prepay for a direct cremation before I CTB. In my case though, it's because I live hundreds of miles away from my friends and family. My step relations aren't exactly close. My other friends and family I haven't seen for 5, 10, some of them over 20 years. I don't want them to feel obliged to travel hundreds of miles for some dry service. They can remember me just as well for however long they want to where they are. I hope they will be ok with that.
In my opinion, funerals are actually quite good for closure and saying goodbye. Despite having plenty of family members die by the time I was 10, I didn't go to a funeral till I was 19. I think it may have actually helped in the grieving process if I had gone to at least one of the earlier ones.
I think in some ways, I get the sense some people want to deny the people around them this. Maybe because they feel like they weren't truly loved by them in the first place. In some ways, it's a way of punishing them I think. I may be well off there, but, that's the impression I get and- maybe they are justified in that.
Sometimes, it's also a hatred I guess for ourselves. I remember one member here saying she told her husband he could just chuck her ashes in the trash. I suspect many of us do feel like this about ourselves but, it's probably quite upsetting for people who care about us to hear.