<< Here is a good one to think about. Persimmon often sets hermaphroditic flowers which are described as “never producing seed” and developing 'parthenocarpically". Ask yourself why these flowers don’t pollinate and produce seed? >>
Based on my reading of the scientific literature, I think you’ve got this wrong. What I’ve read is that hemaphroditic flowers often produce small abnormal seedless fruit and sometimes produce larger normal seeded fruit. Evidently you missed this tidbit in the article from Tao and Ogaki:
<< Hermaphrodite flowers of most D. kaki cultivars or genotypes do not fully function as female flowers because they develop seedless fruit. However, in some individuals, normal fruit containing seeds develop from hermaphrodite flowers. >>
Presumably such hermaphroditic flowers are the “male” flowers that @Barkslip reports fruiting. Indeed, this whole confusion about whether “male flowers produce fruit in persimmons” appears to have resulted from a misidentification of (fruiting) hermaphroditic flowers as male.
But the bigger reality is that nature is not always 100% efficient. If the tendency to produce hermaphroditic flowers is a waste of energy, it probably arose by chance and it may take millennia before “survival of the fittest” eliminates that trait. Or it may be a vestige of something that was once useful, and evolution has not yet caught up. You know, we still have vestigial muscles that once let us wiggle our ears like dogs.
<< Ask another question, why do these flowers produce fruit at all? Then go back and read the articles that attempt to shed light on what is happening. Now ask the important question, why would a tree go to the trouble of producing reproductive structures that can’t possibly reproduce? What does the tree gain from producing fruit sans seed? >>
Given the above, your premise [“can’t possibly reproduce”] is false. Hermaphroditic flowers in persimmons can produce viable seeds.
Nevertheless, this is an interesting question, not unique to persimmons. In persimmons, energy may be wasted on flowers that mostly will not produce. In many species as well, such as persimmons, figs, and bananas, fruit is produced without seeds. Why?
One answer is that in nature, a pollinator is normally present. The persimmon in Asia or the common fig in the Mediterranean has the capability to fruit parthenocarpically but it rarely does, as it is usually pollinated.
A second answer is that parthenocarpic varieties are cultivated by humans! The persimmon or fig in Rhode Island has a simple reproductive strategy – There’s no need for seeds. Just produce tasty seedless fruit and this hedonistic human will manage reproduction vegetatively! Hence cuttings, air layers, grafting, etc.
This last strategy works so well that there are lots of seedless plants that are 100% dependent on humans for their survival. The modern banana is an example. I’m sure you can think of many more.