Why should an API return 'void'?

Question

When writing an API or reusable object, is there any technical reason why all method calls that return 'void' shouldn't just return 'this' (*this in C++)?

For example, using the string class, we can do this kind of thing:

string input= ...; string.Join(input.TrimStart().TrimEnd().Split("|"), "-"); 

but we can't do this:

string.Join(input.TrimStart().TrimEnd().Split("|").Reverse(), "-"); 

..because Array.Reverse() returns void.

There are many other examples where an API has lots of void-returning operations, so code ends up looking like:

api.Method1(); api.Method2(); api.Method3(); 

..but it would be perfectly possible to write:

api.Method1().Method2().Method3() 

..if the API designer had allowed this.

Is there a technical reason for following this route? Or is it just a style thing, to indicate mutability/new object?

(x-ref Stylistic question concerning returning void)

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EPILOGUE

I've accepted Luvieere's answer as I think this best represents the intention/design, but it seems there are popular API examples out there that deviate from this :

In C++ cout << setprecision(..) << number << setwidth(..) << othernumber; seems to alter the cout object in order to modify the next datum inserted.

In .NET, Stack.Pop() and Queue.Dequeue() both return an item but change the collection too.

Props to ChrisW and others for getting detailed on the actual performance costs.

Answer 1

Methods that return void state more clearly that they have side effects. The ones that return the modified result are supposed to have no side effects, including modifying the original input. Making a method return void implies that it changes its input or some other internal state of the API.

Answer 2

If you had Reverse() return a string, then it wouldn't be obvious to a user of the API whether it returned a new string or the same-one, reversed in-place.

string my_string = "hello"; string your_string = my_string.reverse(); // is my_string reversed or not? 

That is why, for instance, in Python, list.sort() returns None; it distinguishes the in-place sort from sorted(my_list).