Sorry... I don't get a rationale about why the tank should be full for the storage matter....
It is a matter of safety if there should be a fire.
In a fire a tank heats up. As the gas inside gets hotter, it increases in pressure.
The idea is that with a full tank the increase in pressure will rupture the burst disk and drain the tank safely before the tank itself would fail due to the effects of heat on the metal of the tank.
With a small enough amount a pressure, even if the tank did rupture due to the effects of fire, there would be little damage or danger to the fire fighters.
There is a more dangerous middle ground. If a tank is say half full, the heating in a fire would not be enough to increase the pressure to the point of rupturing the burst disk. Instead the effects of the fire could cause the tank to rupture. A tank with 1500psi would cause plenty of damage if it explosively failed and could seriously endanger fire fighters.