I'm sorry you lost your dad so suddenly @RedorBlack and this must feel like an extra bit of a kicking, him choosing a Direct Cremation.
I am having one too, and so is DH, and our 2 adult DC know this. They are fine with this, and say they find the thought of going to our funerals unbearable anyway, and will welcome not having to go.
I see no reason to have a funeral personally. One of the main reasons is that I don't want people turning up who barely knew me, and have had nothing to do with me this century, with their faux grieving and sadness. They didn't care about me when I was alive, why bother now I am dead? I HATE it when dozens of people who had nothing to do with the deceased turn up to their funeral. I would not want anyone there who I hadn't heard from/hadn't spoke to in the last 10 years or more. This is one of the main reasons that I am having a direct cremation. No-one in my life (my friends and family and loved ones) needs me to have a funeral. And DH is going to do the same. Direct Cremation.
Plus, a Direct Cremation is much cheaper and much less fuss and hassle than a funeral, and no-one has to worry about the stress and hassle of arranging and paying for my funeral when I die. It will be all sorted. Everyone close to me knows that I am having one. (And DH too. Everyone knows he is.)
I'm sorry you were shocked at your dad not having a funeral though. He should have discussed it with people really.
My good friend lost her brother in March, very suddenly after a car accident. He was only 53. Has 2 children in their early 20s. My friend and the 2 children (her niece and nephew) said they would have given anything to have not had to go to his funeral, and it was so traumatising and upsetting for them. His wife insisted he had a funeral though.
Everyone is different. I know that there is nothing I can do when I'm dead, but it makes me feel very angry and upset and disappointed at the thought of someone deciding to over-rule and disrespect my wishes and have a funeral for me. I do NOT want one.
As has been said, please respect your dad's wishes @RedorBlack 
.