Have block edit distances been computed on large code bases?
I do not know about publicly available tools to do it, but I did fair amount of diff related algorithms and one tool to check similarities between codes.

There are some basics to start with:

0) diff operates well on similar changed texts and falls into worst case when they are different.

1) Tools to check similarities on codes that I have seen, used and written were all operating on AST trees, disregarding formatting, variable and function names. Even though when codes exhibited packaging into functions it gave really hard time. So after that technique like SSA and strip code of functions was applied.

2) Languages that allow same thing to be done in several ways are to be treated as same expressions.

3) Sometimes code is translated into another language. So perfectly working transpilers should exist in first place. Every transpiler I have used was not fully functional, maybe I am not aware of new achievements, but as I checked there is no tool "write in any language you want and get source in any other".

4) There are situations like using well known algorithms, or copying from one book. Also there is probability that two codes are the same, or almost the same (same AST, same language), and are not copied.

5) There might be a lot of false positives, and even if we overcome above problems, what would be the outcome of such search?

There is no tool to produce comparable and working solution to JS. And nowadays many projects are getting JS spin off. Also with tools like emscripten (to operate on LLVM code) makes it virtually impossible to keep track of code.

If you take Levenshtein distance as a measure, you should probably consider above points. This seems convincing to me that it is really not sufficient to start tracking such changes in open source code, as there are tons of them.