As is all too often the case we find that this particular Universe has "values", e.g. Cosmological Constant, Planck's constant = 6.626068 × 10-34 m2 kg / s, einstein's e=mc squared, and so forth.
Other "values" are not available although they must certainly exist under other conditions in other universes. Maybe even the speed of light changes. Randomness, if it were "real", would sometimes select for different values in those constants.
You said, in part: "Random" probably doesn't really exist in our present Universe.
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I am no scientist, and admit so on the front end, but I have questioned the concept of Randomness as well. Certainly much of what we call "random" is just an acknowledgment that we don't know all of the relevant information. For example, rolling dice is said to be random, but if one were to fully describe the position of the dice, the nature and quality of the force imparted upon rolling them, distance to the "landing area," coefficients of friction, etc., one could accurately predict the result of the rolling of dice without fail. That we cannot do so does not make the dice rolling random, except as an admission that we have too little data.
I am too slow to be able to state this as it might relate to evolutionary theory, but I bet someone could (and probably already has). If I have goofed up, please don't think I am somehow ill-intentioned as many have suggested of Coulter. One can be wrong and not of ill-will.