#one can argue that rhaenyra is disconnected from her people and that is one reason why things end the way they do for her

[ladyalicentshightower]

"Team Black is better than Team Green because Luke's funeral is private while Team Green hold a public funeral for propaganda purposes!"

Kingslanding is the biggest city in Westeros and is densely populated, and while Dragonstone is also densely populated, it's infinitely smaller. If Team Black were in Kingslanding instead of Dragonstone, they would never have been able to have a private funeral because the small folk would want to attend too. Furthermore, as an island, Dragonstone is isolated as few would travel for a funeral in a time of war. Kingslanding even during war, has Westeros' highest population density. Aemma and Baelon also had a public funeral in season 1.

In the books (hopefully in the show too), Haelena is remembered as being beloved by the small folk. Jaehaerys, as her son, was loved by and is mourned by them too. Even if they wanted to - and likely they did want to - have a private funeral, they wouldn't have been able to due to public reaction and outcry.