A couple things that explain why this film was so great when it came out:

1. The "Atomic Age" of science fiction. The only sci-fi films I could see on TV as a kid were films like "This Island Earth", "Forbidden Planet" and "The Day the Earth Stood Still" and a bunch that were forgettable . You were lucky if they were in color and not black and white. But the aesthetic of those movies is evident and they took themselves VERY seriously, even when they were obviously over the top and silly.That was virtually ALL you had, in a vacuum, so there wasn't any point of view to criticize them in a way. I experienced Mars Attacks as satire, a little late to the cultural party, but a delicious send-up of Atomic Era sci-fi.

2. The awesome 60's trading cards. My brother and I used to bike down to the local bookstore and buy them when we had money. Here's a sample: https://www.cardboardconnection.com/1962-topps-mars-attacks-trading-cards. (the "bubble gum" was hard and thin and shattered if you bent the stick, awful stuff we threw away immediately) We loved the cartoon violence, it really made an impression on me when TV was filled with war dramas, cop dramas, cowboy dramas which took their violence very seriously, like asserting that it was good and right so they removed the blood so you didn't get viscerally upset and could acclimate to the post WW2 war machine/fascist police state culture. The Mars Attacks violence was like a childish lampoon of modern violence in American culture and I loved it and laughed my ass off.

3. Tim Burton. The over the top surreal and cartoony aesthetic of Tim Burton fit the 40's-50's Atomic Sci-fi aesthetic to a tee if you wanted a satire of the genre, which is what it was. It was Tim's magnum opus as far as a marriage of his personal artistic vision with a slice of genuine American film culture, if a little dated even at the time it was released.

4. Nostalgia for boomers was a big draw, I loved this when it came out and most folks at the time appreciated that it was a satire of a time that was passed but still in living memory.

The RLM guys saying that there was no plot were missing the point, the Atomic Era sci-fi was all aesthetic, it was all about scary science and evil aliens and hating commies, plot was treated like modern porn does.

I can't imagine a Gen X watching this film without all that context. It's a dumb, violent movie that doesn't go anywhere and has a bunch of Boomer cameos...that's what I would think today anyway, but the me I am loved it as a campy satire of a film genre gone by.