I'm sorry, but I'd classify "Farenheit 451" as "Dystopian" and "War of the Worlds" as "Alien Invasion", which are both distinct sci-fi genres.
As a general rule, genres aren't exclusive. Many books and films belong to multiple genres, or belong primarily to one genre but include elements from others. Additionally, many people confuse genre with setting, at least in casual discussion.
Overall I do tend to agree that War of the Worlds probably doesn't count as post-apocalyptic, now that I've had time to consider, but not because it includes aliens. It's not PA because it depicts the apocalyptic event itself, rather than the aftermath or rebuilding. So it's the post- that's the issue.
Of course, the same issue could apply to a lot of books that are generally considered to be PA, which illustrates one of the common problems with any discussion of genre. While genres are important, they also need to be flexible; trying to define genre too finely can cause you to spiral down a rabbit hole into smaller (and sillier) definitions.
PA isn't just when a particular country/society dissolves (ex. Rome, Ancient/Modern Egypt or Modern Syria), but when ALL society rules collapse (i.e. there is no government whatsoever, and it's every man for himself).
That's a very modern definition. Today, most people tend to think globally. We hear about news from around the world almost instantly, have access to shared resources, corporations span multiple continents, and so on. Even within the lifespan of people on this board, though, that wasn't always true. I lived in Peru in the '70s and Ghana in the '80s, and we couldn't make international phone calls with any consistency; we kept in touch with family in Canada by recording audio cassettes then mailing them, and it took months for them to arrive.
So when a person has the world at their fingertips, any apocalypse which isn't global can be worked around. Prior to the 21st century, though, an apocalypse could be as small as a village. If everyone you've ever met or loved died, and you had no way of going anywhere other than walking, how could that not be apocalyptic, even if it's only a few hundred people in one valley?
I haven't seen any real good post-apocalyptic worth mentioning - each and every of them is good idea or novel turned in a terrible mess
I take, then, that you've never seen any of the Mad Max films? Nor anything from the Terminator or Matrix franchises. Planet of the Apes is based on a novel, but some of the films are still quite good.
Nausicaä of the Valley of the Wind is based on a comic, but both comic and film were written by director Hayao Miyazaki. Silent Running, The Quiet Earth, and Snowpiercer are all pretty entertaining. Even some films based on books are good, though certainly many aren't. That's just Sturgeon's Law, though.