The argument for superheroes to capture villains alive is that superheroes are already illegally operating as vigilantes and compensating for muggle law enforcement is all they are morally obligated. The burden of dealing with super villains permanently falls squarely on the justice system, not the the superheroes.
The more dangerous super villains are walking, talking weapons of mass destruction and threats to planetary security. They cannot be rehabilitated nor permanently killed. Keeping them in prisons and asylums that might as well be made of wet tissue paper only puts the public at further risk of mass death and destruction. The only reasonable choice is to permanently seal them inside personalized vaults with the most extreme safeguards to prevent breach (e.g. nuclear warheads), a la the SCP Foundation.
However, a world where governments did this would be a world where conventional superhero plots just can't happen. There needs to be a reasonable justification for why governments and the public at large are perfectly comfortable putting their lives and property at such risk every week.
(I originally asked another question similar to this one, but failed to take into account the unpopularity of the death penalty and superhero/villain immortality. When I changed to question to account for this, it ended up making the answers into non-sequitur. I decided that this question was sufficiently different that it qualifies as a separate question, but I really didn't want to because I had bad experiences with asking chameleon questions in the past. I leave it to the mods to decide.)