Once Kandinsky and other modernists go abstract, the highly reductive Malevich and the Supremacists, and Mondrian find what seemed like suitable end-points for non-objective painting, that is, painting that is so abstract that it no longer has a motif, or represented object.
Mondrian systematically took himself step by step through the whole process, from an initial reduction from representation, through increasing abstraction of that representation from the motif, to the total abstraction of his signature style. At the end of his life, he injects an abstract referentiality, if you will, back into the mix in the final Broadway Boogie Woogie paintings..
Once the abstract end-point is found, it seems to shunt the next generation off into other concerns. To the Modernists, from there, it only remained to find abstract means to paintings that still contained recognizable motifs, or to move to more figurative and hence, pictorial, means, albeit for purposes that still intended to subvert traditional representation, such as the multivariate tactics of the Surrealists.
For Picasso, who lives and flows through several generations, he carries out these swings within his own work. Sometimes within a single day. This has also been a tendency in the current generation [Humphries, Josh Smith, Christopher Wool, Richard Prince, et al.].