Yes they do. Usually in ways that are deleterious to the organism's survival prospects. But on Darwin's theory, "Nature" selects those rare mutations that are helpful to "survival fitness." And this is how speciation occurs.
You asked, "Can you think of any reason why scientists would require that theories be based on something that can be empirically quantified or qualified?"
Because they're only interested in "How?" questions, and not "Why?" questions?
It seems there are all kinds of things in the world that are empirical or phenomenological which can't be either directly observed or quantified. Mind would be a case in point. Indeed, so also is Life itself.
What Darwinism seems to want us to believe is "that the numerous and prima facie improbable physical and biological requirements for life all fell together just by a fluke, like so many dice tumbling out of a bag and landing all sixes," as M.I.T.'s Roger White puts it.
Not so long ago, scientists suggested that the very earliest living organism was the result of a "chance collision of molecules" in a pre-biotic soup, where this was not meant to be incompatible with determinism. I think we have a good enough grip on what they had in mind: some simple molecules were shuffling about in the soup — much like shaking Lego pieces in a box — until they just happened to form a stable structure capable of reproduction. It is this kind of view that is being denied when contemporary theorists insist that life did not originate by chance. — Roger White, "Does Origins of Life Research Rest on a Mistake?"At this point, a good Darwinist will say that Darwin's theory isn't about the origin of life, just how it evolves once it's here. Some ill-defined something is evolving. Which to me is reminiscent of how primitive peoples thought about the issue:
To the ancients, life simply was; it was a given, a first principle, in terms of which other things were to be explained. Life vanished as an explanatory principle with the rise of mechanics, when Newton showed that the mysteries of the stars and the planets yielded to a few simple rules in which life played no part, when Laplace could proudly say "Je n'ai pas besoin de cet hypothèse" [I have no need of that {God} hypothesis]; when the successive mysteries of nature seemed to yield to understanding based on inanimate nature alone; only then was it clear that life itself was something that had to be explained. — Robert Rosen, Life ItselfDarwin's theory is consistent with materialism, reductionism, mechanism. But it doesn't have a word to say about Life; because Life is not reducible to materialism, reductionism, or mechanism. It is not something that can be stated in terms of scientific metrics or differential equations.
But it is definitely empirical and phenomenological.
I join my dearest sister in Christ, Alamo-Girl, in urging you to read Rosen's splendid book! Thanks for writing, tacticalogic!
You appear to be describing abiogenesis. I cannot find that addressed in the Theory of Evolution, and have no compulsion to attempt revisionism to include it.