>we end up performing two loops instead of one, all because sticking three operations in one statement is "yucky"

You seem to believe that "O(2n)"

  for value in range(1, n + 1):
    result ^= value
  for value in A:
    result ^= value

  for value in range(1, n + 1):
    result ^= value
    result ^= A[value-1]

Unless both loops get unrolled it's ever so slightly slower due to having to check for the end value twice. Plus potentially a cache hit at the start of the second loop.

None of this is as straightforward as it seems.

A "for" loop in Python isn't particularly cheap. It compiles to some static overhead to set up the iterator, then each loop iteration compiles to the "FOR_ITER" opcode, a "STORE_FAST" opcode to assign the iteration value to a variable, and the body of the loop.

"FOR_ITER" calls the "__next__()" method of the iterator (which is on top of the interpreter object stack), catches the StopIteration exception to know when to terminate the loop (by jumping past the loop body), and stores the iterator value to the top of the stack. What "__next__()" does is totally opaque - we don't know what kind of object A is - but since we've added the overhead of a function call already it wouldn't matter if it was a super tight bit of machine code, we're already paying a (relatively) hefty runtime cost.

A particularly bad implementation of "__next__()" for some custom iterable collection might be so stupid as to walk through the collection until it reaches the current index's item and returns that, so "for value in A" could in fact be O(n^2).

Plus, "result ^= A[value-1]" is substantially more work than "result ^= value", so even just on the loop bodies the two examples aren't very similar at all. Evaluating "A[value-1]" may wind up calling a "__getitem__()" method on A.

If A is, say, a linked list or binary tree, iterating it is very cheap but indexing it is O(n), so the second loop might be O(n^2) where the first is O(n).

So maybe we be a bit more Pythonic, and do:

    for i, value in enumerate(A)
        result ^= i
        result ^= value

Why would this matter for speed? I don't know. Unless 'n' is pretty big a human won't even notice the execution time of any of this code.

Even assuming python's foreach loop in these cases get optimized down to a very bare for loop, the operations being performed are dominated by the looping logic itself, because the loop body is so simple.

Each iteration of a for loop performs one index update and one termination comparison. For a simple body that is just an XOR, that's the difference between performing 5 operations (update, exit check, read array, XOR with value, XOR with index) per N elements in the one loop case versus 7 operations (update, exit, read array, XOR with value, then update, exit, XOR with index) in the two loop case. So we're looking at a 29% savings in operations.

It gets worse if the looping structure does not optimize to a raw, most basic for loop and instead constructs some kind of lazy collection iterator generalized for all kinds of collections it could iterate over.

The smaller the loop body, the higher the gains from optimizing the looping construct itself.