What is the wisdom behind the punishment for a non-married rapist being only one hundred lashes? And is the desire to increase the punishment considered a violation of Islamic law?

Rape is coerced fornication and an assault on a woman's honor. There are two types of rapists: 1. One who coerces a woman into fornication without using a weapon or kidnapping. This individual is subject to the hadd punishment for zina (flogging for the non-married rapist, and stoning for the married one). Some scholars also obligate him to pay the woman her mahr. If the hadd punishment is not established, the ruler may impose a discretionary punishment (ta'zir). 2. One who coerces a woman into fornication by using a weapon or kidnapping her (whether he committed zina with her or not). This individual is subject to the hadd punishment for hirabah (brigandage), and the Imam has the choice between execution, or execution with crucifixion, or cutting off opposing hands and feet, or banishment from the land; based on the words of the Almighty: (Indeed, the recompense of those who wage war against Allah and His Messenger and strive upon earth [to cause] corruption is none but that they be killed or crucified or that their hands and feet be cut off from opposite sides or that they be exiled from the land.) Al-Ma'idah/33.

In summary, the punishment for rape may reach execution, depending on the details of the crime.