Alcatraz was designed to keep the worst of the worst criminals in one place and well removed from society. That meant it had to be escape proof, and the designers of the prison thought they had cracked it.
The observation towers were strategically placed to be able to see the entirety of the prison and the cell doors were believed to be tool-proof to avoid anyone breaking out. There were metal detectors at doorways and tear gas could be remotely detonated should anything get out of hand. Of course, there were the freezing cold waters to keep prisoners on the island should they somehow break through the prison security measures.