Why is True Altitude calculated using the difference from the QNH to 1013hPa?
Because it is preferable to work with standard atmospheric data,(ISA international standard atmosphere where at mean sea level, the temperature is 15° and the pressure is 1013hPa) 

and because your navigation instruments will display your altitude with respect to a reference, on QNH setting, above the transition altitude the reference is MANDATORILY the mean sea level pressure of 1013 hPa

However it is possible to set your instrument with respect to the field elevation(QFE) so that at landing your displayed altitude is zero.

Airfield QNH is obtained by correcting a measured QFE to sea level using ISA regardless of the temperature structure of the atmosphere. As your altimeter is calibrated using ISA, it will indicate altitude correctly at the airfield reference point. At other altitudes, the indicated altitude is likely to be in error, depending on the temperature of the atmosphere.

All altimeters are based on ISA, notwithstanding instrument error, altitude readouts between aircraft will be similar, whether flying colder than ISA or at higher temperature than ISA, the most important matter is that above the transition altitude you must be on QNH ISA condition(reference:1013 hPa) to insure height separation between aircrafts.