By browsing notebooks on the web, I see that most of the time Ward's method is used for hierarchical clustering. What could explain its popularity? Does it mean that in general it performs better than the other methods?
If we cut at $k=3$ the number of clusters, we see that in the 2D case the Single Linkage can cluster perfectly the first 2 datasets whereas Ward Linkage cannot. In the third dataset, I see that Ward's method is clearly superior to the others. What I suspect is that people assume most of the time real data to follow the geometry of dataset 3, thus explaining the popularity of Ward's method over the others.