Trump's idea will bring the United States back to when it was serious about law enforcement and didn't hesitate to lock up dangerous criminals far from society. If Democrats' hand-picked judges continue to block the Trump agenda, the administration has no choice but to find other places to detain the dregs of society. This is the way it's supposed to be in a rational country.
Trump is just trying to get a rise out of Americans with this fundamentally unserious and impractical proposal. The United States doesn't need Alcatraz because it already has functioning maximum-security prisons. Rebuilding and enlarging the prison would require extraordinary expenditures at a time when the administration plans to cut billions from federal law enforcement.