In a typical 60 Hz power transformer intended for sinusoidal waves an excitation of between 5 and 10% is acceptable. So, the 3% you measure (assuming you are measuring it correctly and under correct conditions) is reasonable. However, if you are driving the primary with square waves as in a typical inverter topology, the classic sinusoidal excitation rules of thumb are not quite applicable because of the high frequency components of the square wave excitation.
The exciting current is not considered a loss because it is in quadrature (90 degree phase shift) from the excitation voltage. Under open circuit secondary conditions the primary and the core essentially form an inductor. There are both copper losses due to the excitation current flowing thru the primary winding, as well as iron losses due to magnetic flux flowing in the core, even when the secondary is unloaded. If you are driving the primary with square waves, a normal 60 cycle iron core will loose more energy to heat than it would with sinusoidal drive due to the higher harmonic content of the square wave. So, you should choose a "better" material for the core to improve efficiency and avoid overheating the core.
"Maximum theoretical efficiency" would be 100% if the theory assumes lossless iron and Ohmless copper! Not likely in the harsh, cruel world of electronics reality in which we exist.