I believe that preservation of “color purity” or “saturation” is a by-product of the threshold, not the compression function.
Tanh happens to maintain saturation at a high level because the initial slope is steep.
However, if the threshold is set with the intention of preserving high saturation, the same result can be achieved with the simple Reinhard compression function.
Here’s an example using the beautiful lambertian sphere 
This is the original with out of gamut values rendered through the ACES Rec.709 view transform.
Here’s the same image with tanh cmopression, with a threshold value of 0.4.
And the same image with Reinhard compression with a smaller threshold of 0.21. Note that the color purity of the blue sphere is pretty similar to the tanh compression curve.
(As a side-note if you look closely at the left cyan blob you can make out the more sudden transition of the Reinhard curve. I’m not sure if this is a by-product of the lack of C2 continuity or just the more abrupt transition of the curve from linear to compressed.)
And finally here’s a plot comparing tanh and reinhard.
Note that distance here is a parameter that specifies the distance beyond 1.0 to compress to 1.0. So a value of 0.24 compresses a distance of 1.24 to the gamut boundary.