How about Leaving Las Vegas? Fantastic movie.
Tommy and Hair were turned into great movies.
Broadway has Mamma Mia!
Supposedly the working title was 3000 for the dollar amount he paid her for the week, but Garry Marshall thought it sounded too science fictiony.
That was the original title, and the overall tone of the script was much darker and had a more realistic ending. Then it got Disneyfied!
Dazed and Confused is a great movie. Does the song count as a pop hit?
Another Julia Roberts movie: Something To Talk About.
not so good
Yes, and so does Can’t Hardly Wait. 
A little on the silly side–especially the nerdy male Beatles fan, who is channelling Jerry Lewis throughout–but I love it.
RickJay, A Hard Day’s Night was not named for the song. Lennon and McCartney wrote the song to order after the title had been decided.
Mystery Train is a great film.
For non-rock ‘n’ roll “pop songs,” there are Round Midnight and De-Lovely.
Well, if we’re counting movies whose title songs were big hits, there are things like Goldfinger or Live and Let Die. Not to mention all film versions of Broadway musicals. But I don’t think the OP means the songs were created for the movie (or that the movie inspired a popular song, like Key Largo).
However, the Gene Kelly An American in Paris would qualify.
Brazil, where hearts were entertaining June…
We stood beneath an amber moon…
Tell me that’s a terrible movie and I’ll poke you in the eye!
Just Like Heaven wasn’t too terrible, for what it was.
Well, okay, yeah it was. Only goes to reinforce the OP’s theory.
Blue Velvet
I am absolutely sure Pretty in Pink was a song first. I’m also sure the song (and the remake used in the movie also made by the aformentoined Furs) is not as good as the orginal, or the movie as good as the original video.
Seven was pretty good.
Wait, that wasn’t named after the Prince song? Never mind…
Love Potion No. 9 had its fair share of chuckles. Tate Donovan and Sandra Bullock star as two nerdy research scientists who unknowingly create the most power aphrodisiac the world has ever seen.
Wasn’t Star Wars named after Nick Winter’s song?
It’s worth noting that the song White Christmas was actually introduced 12 years earlier, in the 1942 film Holiday Inn, which is (imho) a much better movie.
I came in here to post I Wanna Hold Your Hand, but Reality Chuck beat me to it.
Not a great movie, but a sometimes charming and funny comedy about Beatlemania in the U.S.
May I add to your corollary my own Subsection D (AKA the Disney clause)? If Artist X and/or Artist Z are actors from the movie, the movie will suck more ass than a Boeing 747 taking off through an atmosphere made up of pure donkey.
I am trying to remember the lyrics, could you dance to it?
Who’ll Stop the Rain - not a formulaic comedy and not terrible, in fact one of my favorites.