The reason for this is the 'guillotine ' own function: kill more people in a shorter time, and with the minimum effort involved. Traditionally, nobles are sentenced to beheading for being considered the most honorable form of execution. It is on the French revolution that the guillotine was implemented. Many nobles to be murdered, swords should be used, it probably took a lot of physical effort to cut off a head. That's how they created the guillotine, which ended up being used for executions of all types of classes due to its functionality, and for already being there.

In the United States there was no such need, so it would not be logical to build this structure to kill one person or another.