line drivers were originally intended to drive lots of long cables to lots of amplifiers. for a variety of reasons, normal HU outputs may be unsuitable for driving cables of several hundred feet, or connections to over 10 amplifiers. A line driver also contains an internal power supply in most cases, removing output voltage limits.
desired features of line drivers are often the lower output impedance and higher voltage capabilities when compared to a HU's output. These can become important when you have LOTS of amplifiers, or VERY long cable runs. such conditions would be much more common in pro-audio.
Because the input signal merely controls the amplifier, the reasoning of "runs cooler" is flawed. the parts of the amplifier that cause it to get hot are very closely tied to the parts that must handle high currents. the "voltage gain" really takes next to 0 work. From a purely technical standpoint, the line driver might cause an increase of around 5 thousandths of a watt of power dissipation.
reports of SPL gains and improved efficiency are more likely attributed to the re-setting of the gains.