Because it's old fashioned. It's adult without "being adult", over sexed, and otherwise offensive.
It doesn't rely on a lot of BS shaky cam and asinine dialogue or editing. It's a musical, but isn't too over the top for a musical.
It's an exaggerated biopic about the nicer sex, and as such the film is nicer. There're no real tense moments, no real uncomfortable moments, and it's kind of honest.
It's a pleasant experience to pass the time. Verse something like "Mad Max 2; The Road Warrior" which is a film I love, but it's like watching high energy action Shakespeare.
It comes from a time when film making was simpler, but no less care went into it, yet fewer tricks were used. Performances carry the film in this era, as well as natural spectacle, instead of SFX dazzlement, which gets tiring.
Hope that helps.

I really enjoyed how thoroughly Debbie threw herself into it. She wasn't afraid to get dirty or undignified. It was like she was finally able to be herself and play.

I love it, I checked into it on a whim after seeing a couple clips of it on Turner Classic Movies as Debbie's daughter, Carrie Fisher, was talking about how she often fought in the films and how she acted a lot at home like in the movies.
I have quite a few favorite parts to it, the most particular one is when Molly first introduces the men at Christmas' bar to "Belly up to the bar, boys!" She was terrific on the piano and even when she stopped she had an amazing voice, and while her dancing isn't anything specactular and difficult like when she danced alongside Donald O'Conner and Gene Kelly, it's still great dancing that she does, of course this dance is an easier one for the people at home to probably try and imitate.
I also love when Molly and Johnny get their fancy home but they're still not 'cultured' and they yell through the entire houseI just love it when Molly's putting on her shoes and yelling "I'LL BE RIIIIGHT DOWN!" I also love it when they crash the snobs' party and make everybody's jaws good as drop when they donate $15,000 to the clergyman.
When Molly's plans for her new life go awry and she unloads two shotgun shells at the tour bus passing by, it's hilarious to see her go off the deep end like that.
Then when she's among the many in the lifeboat after escaping the fated Titanic and she's the only clear head in the whole bunch who insists that panic won't get them anywhere and they're going to be allright, you can't help but love it when she's pulling everybody together and says "I'm not ready to die, hell I'm just learning how to live!" Though I do wish like the play, they would've put in the movie explanation that Molly Brown had everybody in the lifeboat rowing for 7 and half hours straight, I think that could've added well to her strong character.

You are so right, chett; it was/is a great movie. I was only 12 years old when it came out at the movies and my whole family loved it. Then, we had to be happy with the TV networks showing it periodically.no VCRs back in those days! When VCRs first came out on the market, TUMB was in the very first group of movies I bought! My mom still loves this movie and I play it for her at least once a month, sometimes more often. No matter how many times I've seen it, when it's on I have to stop and watch it.as if I've never seen it before! I loved it all.the cast, the sets, the music, the script, the costumes, etc. and overall it is still one of my best "feel good" movies. And remember back then, most movies at the theatres were "double features" but I can't remember what the second movie that played was.