Reaching the smoke point is undesirable for any oil used in cooking because it changes the chemistry of the oil in an undesirable way.
There are studies that claim that all extra virgin olive oils have a smoke point of 300 degrees but such studies ignore variable factors such as chemistry and freshness, which affect the smoke point. The truth is that the smoke point of an extra virgin olive oil will depend on its unique characteristics.
Supermarket olive oil, although labeled as “extra virgin olive oil”, is often poor quality oil in reality, a result of lax processing standards, age, UV light exposure, and poor handling. These poor quality oils tend to be highly oxidized and/or rancid by the time the consumer purchases it. Highly oxidized and/or rancid olive oil lacks the protective chemistry that would otherwise allow for heating at higher temperatures before reaching the smoke point.
Fresh extra virgin olive oil of superior quality (containing high oleic acid content, very low FFA, and robust phenol count) can be heated to greater temperatures before reaching the smoke point.
If you are looking to heat extra virgin olive oil up to 400+ degrees, pay close attention to the chemical make-up and choose one that is very fresh and chemically robust.