For the record, the movie was comedic but the book was not.
I think Heinlein actually has a very interesting point. To wield the power of the government (which is what voting is), it is important to be able to act selflessly. If someone can't do that, even for a couple of years of their life, why should they be able to wield that power over others? The universal franchise is not a religious dogma, it's good to ask these questions and think about whether our society could be better if we organized it differently. Unfortunately, a lot of people completely missed the point and just rounded it off to "Heinlein thinks the military should run society", which isn't at all true.
In the book it was said that if a blind deaf person in a wheelchair volunteered for service, the state would find something for them to do. Maybe tediously counting hairs on a caterpillar, or testing chairs in Antarctica.
Now for me the asspull from Starship Troopers that I still think about every now and then was the notion of mathematical proofs of morality at a high school level (or any academic level, for that matter). This was a society that somehow discovered provable objective morality, and I really wish that idea could have been fleshed out more by Heinlein.
You see him put much more thought into political systems and economics in other books like The Moon is a Harsh Mistress, Stranger in a Strange Land, or For Us, the Living.
[1] https://www.nitrosyncretic.com/pdfs/nature_of_fedsvc_1996.pd...
It was not even the premise of the film - only one right was conditioned on service, the right to vote (and possibly hold political office). I.e. actions that wield authority over others. I argue that is not "basic".