Thank you for the thoughtful and detailed response. I think I have a better understanding. (But, I'll always stay mindful of the Dunning-Krueger effect... ;-) )
BTW, this statement captures something I was trying to express more clearly than I stated it:
(Actually it tends to be the other way around - we see islands of conserved sequence, and deduce therefore that they have a function. This isn't how genes are detected, as there are more sensitive gene-specific ways of doing this.)
What I was trying to get at was that if a section of DNA performs some useful function, even if we don't know what it is, it'll tend to be preserved because selection pressure will tend to preserve it by "selecting out" individuals whose mutations tampered with it. The observed long-term mutation rate for any given point should in some sense be inversely related to that point's significance. (More significant => fewer mutations, likely by a function much more stark than just "1/x", where "x" is significance. Key proteins should have a really strong bias to remain unmodified in viable offspring, for example.)
I now have a slightly different question: You mentioned the rate of repeated mutations, where the same piece of DNA was mutated twice or more, sometimes back to its original state. Suppose the environment shifts, such that selection pressure would favor a certain set of mutations to adapt a species to that new environment, and then the environment shifts back. I'm thinking fairly long term, cyclic shifts such as ice ages and the like.
Would such cyclic shifts meaningfully affect the assumptions underlying the multiple mutation rate? You gave this example: "if you compare two sequences and they differ in 10% of sites, it is reasonable to think that 1% of sites have actually mutated twice." I realize you mentioned it was oversimplified. It jibes with a basic knowledge of statistics and statistically independent random variables. I guess what I'm getting at is that cyclic shifts that affect which mutations improve, decrease or are neutral with respect to fitness would imply at least some of the variables aren't independent.
I guess it comes down to what fraction of the mutations actually affect fitness with respect to these cyclic forces. I imagine it's a fairly small proportion relative to the total set of mutations whose fitness effects are completely orthogonal to those long-term cyclic changes. If that's the case, am I correct thinking the effect wouldn't be large?
I guess in general, if the total delta between two samples is still relatively small (10% in your example), any second order effect such as this could only affect that approx 1%, and so that already bounds the potential error from simplifying assumptions anyway.
Again, thank you for your helpful (to my understanding, at least) response.