Yup, pretty much. Wood begins to char at around 450°F (~233°C) and the vast majority of cooking occurs closer to the 350-400° range. And even at 450, it still takes several hours for wood to char and eventually ignite.
If you were cooking at like 700°, then yeah you’d have issues. But cooking at 700° would be way past the point of Maillard reactions, (the chemical reactions that cause meats to brown, crisp, and add flavor as they cook) and would go straight into char. So even when doing high-temp things like searing steak, it would be overkill because you’d just have a charred carbon crust instead of the nice brown Maillard reaction crust that steak lovers want.