Why does C++11's lambda require "mutable" keyword for capture-by-value, by default?

It requires mutable because by default, a function object should produce the same result every time it's called. This is the difference between an object orientated function and a function using a global variable, effectively.

Your code is almost equivalent to this:

#include <iostream>

class unnamed1
{
    int& n;
public:
    unnamed1(int& N) : n(N) {}

    /* OK. Your this is const but you don't modify the "n" reference,
    but the value pointed by it. You wouldn't be able to modify a reference
    anyway even if your operator() was mutable. When you assign a reference
    it will always point to the same var.
    */
    void operator()() const {n = 10;}
};

class unnamed2
{
    int n;
public:
    unnamed2(int N) : n(N) {}

    /* OK. Your this pointer is not const (since your operator() is "mutable" instead of const).
    So you can modify the "n" member. */
    void operator()() {n = 20;}
};

class unnamed3
{
    int n;
public:
    unnamed3(int N) : n(N) {}

    /* BAD. Your this is const so you can't modify the "n" member. */
    void operator()() const {n = 10;}
};

int main()
{
    int n;
    unnamed1 u1(n); u1();    // OK
    unnamed2 u2(n); u2();    // OK
    //unnamed3 u3(n); u3();  // Error
    std::cout << n << "\n";  // "10"
}

So you could think of lambdas as generating a class with operator() that defaults to const unless you say that it is mutable.

You can also think of all the variables captured inside [] (explicitly or implicitly) as members of that class: copies of the objects for [=] or references to the objects for [&]. They are initialized when you declare your lambda as if there was a hidden constructor.

I was under the impression that the whole point of capture-by-value is to allow the user to change the temporary -- otherwise I'm almost always better off using capture-by-reference, aren't I?

The question is, is it "almost"? A frequent use-case appears to be to return or pass lambdas:

void registerCallback(std::function<void()> f) { /* ... */ }

void doSomething() {
  std::string name = receiveName();
  registerCallback([name]{ /* do something with name */ });
}

I think that mutable isn't a case of "almost". I consider "capture-by-value" like "allow me to use its value after the captured entity dies" rather than "allow me to change a copy of it". But perhaps this can be argued.