When a load is inductive, it simply means its impedance rises with frequency, and therefore draws less current with the same voltage amplitude as the signal frequency goes up.
The job of a speaker amplifier is to output a voltage that follows the voltage of the input, multiplied by the gain, while being able to supply whatever current the load draws at that output voltage. If the amplifier cannot provide the required current, the output voltage sags and we have clipping, just as what
@RayDunzl said in post #86.
A "slow" current rise through an inductor has nothing to do with "speed" (of the supplied voltage). It is the result of the lower current draw by the high frequency components of the step versus its lower frequency components. If you look at the waveforms of the current, they are all going to look the same for any amplifiers with sufficient frequency bandwidth (and voltage and current capacity) to reproduce the step.