Local anesthetics cease to have any effect when they enter the bloodstream. From there, they are as harmless as a piece of fruit in the bloodstream. Most drugs need to enter the bloodstream to be effective. However, local anesthetics are only meant to affect one small area of the body. When a drug is in the bloodstream, it affects the entire body. If the dentist only wants one part of the mouth numb, it doesn’t make sense to make the entire body numb.
Therefore, the difference between local anesthetics and other drugs in dentistry - and other medical areas - is that the local anesthetics break down and cease to have any effect whatsoever once they are in the bloodstream of the patient.