Is const-correctness paranoia good?

Yes, definitely. Lets see this simple example:

$ cat test.cpp
int test(int x) {
 if (x = 1)
  return 42;
 else
  return 0;
}
$ g++ -c test.cpp
$ g++ -c -Wall test.cpp
int test(int x) {
 if (x = 1)
  return 42;
 else
  return 0;
}

Only when we turn on warnings, compiler tell us about a possible error. Making the parameter const shows us error:

$ cat test2.cpp
int test(int x) {
 if (x = 1)
  return 42;
 else
  return 0;
}
$ g++ -c test.cpp
test2.cpp: In function ‘int test(int)’:
test2.cpp:2:8: error: assignment of read-only parameter ‘x’
  if (x = 1)
        ^

All input parameters should be const, all write-once variables serving as a parameters for some computations should be also const.