Me and DH are doing something similar. Direct cremations actually. (Already paid for.) Our adult children and their partners know about this - and are fine with it.
It's not so people don't have to go miles and miles across country to come to our funeral. It's because we don't want people who haven't been fucked with us for the last 10 years or more, and don't give a shit if we live or die (and don't actually know if we're still alive even,) coming to our funerals and pretending that they care.
Basically showing their face for the funeral and the 'wake' afterwards, and staying on to see if there's anything in the will for them. I don't want anyone that's not been bothered with me for more than 10 years, turning up to my funeral with their fake mourning. (And neither does DH!)
I hate it when people attend funerals of people they've had naff-all to do with for more than a decade. You didn't care about them when they were alive, why do you suddenly care now?
Also, turning up to a funeral of a person you didn't know? WTF is that all about? Why do you assume they would want you there?
'I've come to pay my respects' some people say. LOL yeah sure Jan. I bet you don't even know what that sentence means.
As for the 'funerals are for the ones left behind' brigade. It's MY funeral, MY decision. And it's already booked and paid for. (Direct Cremation... Me and DH.) As I said, our 2 adult DC are fine with this.
I'm pissed off with the comment 'your family should be allowed a funeral after you have gone, funerals are for the living lalala' when someone says they are having a Direct Cremation. No-one ever bashes people who say they are having a big funeral, and says 'why don't you just have a Direct Cremation?!'
Leave people be. Respect their decision and quit slating them for it. People have very personal reasons for wanting Direct Cremations. Stop trying to make them feel like shit by demanding they have a big funeral for the world and his wife to attend! 