My research did not stop there. A variety of questions had occurred to me during the writing which I picked up afterward, again, in the library. I chose to answer this question for the Cnidaria, since I was already acquainted with several members of this phylum. Cnidarians are also suitable subject matter, since many exhibit both forms of reproduction. In retrospect, this answer is not surprising, since asexual reproduction is a phenomenon of epithelia, while sexual reproduction is a phenomenon of amoeboid cells.
Epithelia is a steady-state type tissue, while amoeboid cells exhibit stem cell dynamics.
Other differences between epithelia and amoeboid cells are documented in the experimental literature of both Hydra and larval marine hydroids. In order to pursue this hypothesis, I decided to trace the evolution of cnidocysts, since a large literature, going back nearly a century, already exists on their distribution in different taxa. With the assistance of interlibrary loan, I accumulated comprehensive data on the qualitative and quantitative distribution of thirty or more types of morphologically defined cnidocysts in nearly a thousand species. These data are now available to the public as a cnidocysts database. Differences in the range of cnidocyst diversity, moreover, suggest that competitive exclusion and character displacement influenced cnidocyst evolution in Medusozoa.