This photo tells a big story: The highest heat level from the fire is near the ceiling, right where the transom is located. The transom is the glass window above the door. They were designed to allow light to enter a space. If able to be opened, they allow air to pass from one space to another. This was a common building feature before air conditioning, rising crime and changes to the fire code.
In the photo, the firefighters are in the public hallway of a multiple dwelling adjacent to the single-egress stairway. The transom failure allows both smoke and more importantly, fire, to enter the public hallway and stairway. This is a major life safety concern at any fire in a multi-floor building with an open interior stairway. The first line must go inside to protect these spaces, transom or not. Smoke will migrate into the interior hallway and stairway; however fire migration must not occur.
While transom failure can allow for water application, its failure prior to hoseline placement is the threat. This building feature is now rare on apartment entry doors. Changes to multiple dwelling fire codes in most locations eliminated this building feature.
Homes that contain interior transom windows or high open spaces between rooms or rooms and hallways are candidates for early fire extension. I have traveled down hallways past transoms to get to the fire room entry door to extinguish the fire. While you are passing fire, you are not passing the fire room. Typically, the transom is releasing high level heat, relieving the room entry door of this function.
Tactical extinguishment choices should be based on experience and conditions present. Protect public egress spaces first. Once inside, use your knowledge to extinguish the fire.