Why are stepper motor phase currents a sinusoildal waveform?
The sinusoid shown in your question is related to the position of the stepper motor between its base detents it has nothing to do with the current through the phases or the speed (rpm) of the motor. The frequency of this sinusoid can be reduced to DC, in other words the motor is stationary. 
Look at something like the TB6600 datasheet to understand the difference between the position current ratio (relative to two phases) and the switcher current (relates to only one phase).
One describes the relative ratios between the currents in two phases (but has nothing to do with absolute values, stepper motor phase inductance or resistance), while the other describes the actual phase current in one phase. Consider that the same driver can drive a stepper motor with 0.5A peak current and stepper with 2A peak current.....the position ratios do not change.

Stepper motor currents DO NOT have to be sinusoidal, but the ratios between phase current must be sinusoidal. This depends purely on whether you micro-step or not.
Micro-stepping allows you to position the motor between its base step positions. For example a 1.8deg step motor can be driven at 4, 8, 16 ….256 times it's base step resolution. Start reading: 


Micro-stepping as it relates to per step torque
Switching frequency as it relates to per phase current


Notice that in #1 the torque collapses rapidly as you increase the micro-step ratio. Consider that at any point in the position domain the change in current through the two phases drops, so effectively reducing the power available to turn the motor armature. 

You DO NOT need to have a switching driver for the per phase currents. There were many disk drives in the early days that did head positioning with stepper motors, but they used a D/A with a constant current driver to set the current per phase. 

If you want a good reference for understanding stepper motors and the drive technologies you can't do much better than Paul Acarnley's book STEPPING-OTORS A GUIDETO THEORY AND PRACTICE.
In particular, sections 3.4.2 and 3.4.3 and 5.4.4 will be of interest to your question.