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.
Super villains are domestic terrorists. All attempts at rehabilitation (other than brainwashing and lobotomies) end in failure. Keeping them in prisons and asylums they will inevitably escape only puts the public at further risk of mass death and destruction.
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.