This is coming up because of the Tennessee "firefighters watched it burn over $75" story. But there's backstory to that story. The fire department in question served a nearby town, and had no responsibility for the area where the fire occurred. As a service to people living outside their area, you could pay $75/year to get "out of area" coverage. The people who lost their house did two things to keep them from being…
I suspect the firemen went there to asses whether there was 1)a high degree of danger to lives of people and 2)uncontrolled spread of the fire.
If there were people in the house, they would have more than likely used their expertise voluntarily to extract those people from the flames. But a house is just a house, even with sentimental value. (My dad is a bit of a hoarder and literally has junk that he holds on to because of "sentimental value.")
All in all, the priorities of the fire department were on the straight.