There is a practical reason to the grass directly around your home, like you said, to deter rodents and insects. However, that is not the real reason. The real reason is property value. Untrimmed grass supposedly makes the neighborhood unattractive for people buying homes. Local municipalities get pushed into making petty ordinances to maintain property value for sellers and real estate businesses.

Using the excuse of property value is how a lot of nasty local laws get made. A lot of the terrible anti-homeless action you see in places like LA come from the argument about property value. Safety and sanitation is only thrown in after the decision has already been made.