In the operating room at a hospital, general anesthesia is the norm. This is administered by an anesthesiologist who has years and years of postgraduate training and experience with doing only anesthesia. Most dentists prefer not to put in an IV because it is expensive both from the insurance standpoint and otherwise, and most of us have never done the procedure. Most dentists don’t do anything invasive enough to justify it and honestly aren’t interested in doing it. There are significant risks from general anesthesia, such as death. Local anesthesia in dentistry will only kill you if you have significant health issues and you get too much epinephrine, which is easily preventable.
In reality, anesthesia in the hospital doesn’t always work the first time. My wife’s first epidural didn’t work and that was extremely unpleasant. Dentists just get more of a bad rap for how we administer local anesthesia, and most dentists could do a little better to make it less unpleasant.