This is a misconception. Gluconeogenesis and ketogenesis occur together in the liver. They are both inhibited when carb intake is high, they are both stimulated once carb intake drops low enough. Yes, the liver uses amino acids to produce what little glucose the body actually needs, plus a glycogen store to pump out to the skeletal muscles at need, but that process is more tightly regulated than the myth that excess protein automatically gets turned into glucose implies. The body is more sophisticated than that.
Someone who is eating enough fat probably has very little need for gluconeogenesis, other than what the brain and the red blood corpuscles require. However, the body’s stress response and other physiological processes cause serum glucose to rise, because it’s what fuels a rapid, explosive muscular response. Ketones are better at fueling endurance. The difference is between fighting off a sabre-toothed tiger that has invaded the cave and chasing down a woolly mammoth or an elk. The inflammatory response to injury or infectious disease can also raise serum glucose, I believe.