It should be remembered that Clyde Barrow (and several other notorious outlaws of that period) declared repeatedly that they would never be taken alive. Clyde also made an ongoing sport out of taunting the newly-created FBI in letters to both Hoover and several prominent newspapers. He also reportedly sent a letter to Ford Motor Company endorsing the new V8 motor that allowed his gang to escape and evade law enforcement.
Communities throughout the Midwestern states lived in constant fear of raids by the "automobile bandit" gangs. In addition to bank robberies the gangs frequently started out by cutting telephone and telegraph lines, then taking over entire towns at gunpoint. Many towns constructed bunkers and blockhouses stocked with Thompson guns and Browning Automatic Rifles in hopes of defending their populations from these brazen attacks.
J. Edgar Hoover's reported orders were to "shoot on sight" many of these outlaws like Bonnie & Clyde, Baby Face Nelson, John Dillinger, and several others. The situation was basically open warfare between notorious gangsters and civil society.
Laying in ambush with rifles and automatic weapons to engage an automobile believed to contain Bonnie & Clyde may strike us today as an extreme measure. Shooting John Dillinger as he left a movie theater on a crowded city street, reportedly without any warning or attempt to arrest, is another example of government actions that would likely cause public outcries today. Apparently not the case in 1930s Depression Era America. Perhaps the only rational way to respond to the threats against public safety.
Welcome to modern 21st Century society! Street gangs, international terrorists, human trafficking, and revolving door courthouses. Bonnie & Clyde could probably live very nicely on their book royalties and movie rights, with the right attorneys of course.