If you manage to achieve a sine wave then you are just lucky.
It has nothing to do with iron saturation. A single coil in a slotted core will tend to produce something approximating to a square wave. The flux will link the coil for a significant period as the magnet crosses, at which point there is no change in voltage.
As the magnet approaches and again as it leaves the slot the flux will snap from one tooth to the other and link the coil. This will give a steep voltage change.
With a real winding several factors tend to smooth things off, firstly you may have several coils adding voltage at different phase angles ( distributed winding) and secondly it is unlikely that your magnet system will give the field of a curved continuous magnet.
How these factors add up will determine the final wave shape.
If you are charging batteries there is no need for the waveform to be a sine wave, the low harmonic frequencies are far too low to pass through the battery which acts as a large capacitor.
The only ill effect might be that you run into circulating currents with delta connection that will cause drag at start up. If these are single phase machines it will not matter and for 3 phase star it doesn't matter. In fact with star the line voltage is likely to be far better even if there is a lot of odd harmonics on the phase voltage.
Air gap machines ( axials) have no flux snapping as there is no toothed core, the width of winding inherently causes a distribution and unless you choose the proportions really badly they give at least a line voltage that is often almost a pure sine.
Flux
