Werner's cardioid projection is the limiting case of Bonne's projection when the standard parallel is a pole:
This projection is usually classed as pseudoconic rather than pseudoazimuthal, as would seem consistent: instead, the term pseudoazimuthal is used for more exotic types of projections, such as the retroazimuthal and loximuthal projections, and possibly also the Gnomonic when it is compressed along an axis to allow two points along the axis to serve as centers of the projection.
It has an attractive appearance, but is little used except as a novelty, particularly considering that it puts the area of minimum error in a part of the map that is unavoidably interrupted.
However, there has been one notable development of this projection. J. Paul Goode, who originated the idea of interrupting the Sinusoidal and Mollweide projections, and then developed the Goode Homolosine projection, also used Werner's Projection as the basis of the Goode Polar Equal-Area Projection.
This projection dates from 1928. The illustration below is from an paper he wrote for the April, 1929 issue of the Monthly Weather Review:
There are numerous "kinks" in this projection, a characteristic I tend to find objectionable. But they are almost unavoidable, without accepting a great amount of mathematical complexity in the design of a projection, in order to achieve the goals which this projection has achieved.
It is equal-area; the shapes of nearly all the continental areas are well-preserved, with only Africa falling a little short; but, most importantly, the various land masses are shown in their proper relations to each other, at least in terms of the places where they are either connected by land or not separated too far by sea.
The major field of application of this map projection, therefore, is to facilitate the illustration of information related to the field of geopolitics.