That seems to always be a double-edged sword. The purpose of a relocation is to cover an unprotected response neighborhood. Now, the chief needs additional units - NOW! Do you use units from a further distance that will take longer to get there, or do you use the closest resources and again - relocate units to cover open response areas? the key word here is "NOW"
An old fireground adage: If the chief is requesting additional units, he probably needed them 5 minutes ago.
Actually, I just now saw FDNYSTATENISLAND's post above - same logic.
I agree with you. Closest unit goes. But remember, other units are moving up to cover stations, so in theory, and usually actuality, no neighborhood is left stripped for very long.
Example: A 5th Alarm is struck and the engine from the closest station is dispatched. Not too far behind them, at a close station is another covering engine which will move into the now vacated station. And the parade continues, with other units from farther away start getting fed into the pipeline toward the fire.
Here is not what happens: Engine 1, 2, 3, 4, 5 are at the scene. They don’t dispatch Engine 6 & 7 from 12 miles to the scene on the next alarm! Rather Engine 6 may be in Engine 1’s house, Engine 7 may be in Engine 3’s house, Engine 8 may be Engine 5’s house and Engine 9 may have moved up to Engine 7’s house. It‘s really a logistics problem that doesn’t have anything to do with firefighting per se. FDNY can probably move 100 pieces and still provide reasonable coverage for the city. In the example I gave above, if the department has 10 engines, if the fire continues to grow you get into mutual aid. Town X, Y, Z may each send an engine to cover empty stations in the town that has the fire.
If you look under “Fire Operations” I expanded on my thoughts under “Apparatus Relocations”