Becasue there's only a limited number of ways to make a living. The same was true in the past. The players change, the game remains the same.
Yet plants never seem to have evolved into any niche that required independently directed motion.
Because they have evolved superb adaptations to fill the niches they fill. As have animals. Any open niche requiring independent movement would be first filled by an animal because it has a head start in the game. If you were to pose the question, "why don't animals fill niches that require photosynthesis?" the answer is the same, but reversed. Because plants are highly evolved organisms especially adapted to fill that niche.
And sexless organisims never seem to have evovled much at all -- yet they have avoided erradication by animals or plants competeing for their niche.
I am not sure what "sexless organisms" you refer. If you mean asexual organisms, such as bacteria, you are mistaken. They have clearly evolved. Futher, they are some of the most successful organisms on earth. Except for human bias and the accident of our lineage, we would instinctively know that the history of life on earth is the history of bacteria.
There seems to be a general favoring of sexual reproduction among multi-cellular organisms above a certain size. However, whether that is the result of competative pressure, a relic of history, or some combination of the two is still open to debate.
There is one HYPOTHESIS -- hard to raise it to the level of theory -- that the random mix of natural physical processes operating under strict darwinistic evolution would for complex and subtle reasons unknown at this time result in such a current state. That is a HOPE, a FAITH, a BELIEF SYSTEM.
This statement does not make sense to me. Perhaps you could restate it. Religion is about hope, faith and belief. Science is not. Evolution is about science.
It is unproven. It is not a reasonable projection of more proven and evidenced theory either -- not reasonable, that is, if it is asserted as the ONLY reasonable projection.
Not really. The science of biology and especially evolutionary biology is often the study of why certain organisms fit certain ecological niches in the manner that they do.
They are not orthogonal sets. Science ALSO employs -- esepcially in biology and paleontology -- considerable amounts of hope, faith and belief. Likewise "religion" employs far less of them than you might thing. Both are about organizing things, how best to organize things. Nor need they be competitive.
A little language lesson. Often what the "a" in front of terms is derived from latin -- many times it means "absense", less frequently it means "to". (Ad infinitum). In "asexual" it means "absent of sex", or "sexless".