This is a great question. There are a few important points to be made.
First, there are some wildfire that need to be stopped at all costs. This is so when the life of people and their way of life is threatened. Recently, this happened in New York State and even New Jersey (last week and this week). The firefighters valiantly stopped the spread with minimal loss.
Second, when fires are started by carelessness or worse intentionally, these too should be stopped as well. In these cases there is a risk that people will get hurt, because they do not happen naturally.
Third, there are some wildfires that happen naturally. When this happens, it is difficult to know what to do exactly. The reason for this is because wildfires are a way nature gets rid of unnecessary excess and creates for life to take place in time. Ironically, these wildfires promote life and even wildlife. These ecosystems are called fire dependent ecosystems. In these cases, we should leave the decision to the experts.
Finally, I will add a link to Smokey the Bear.