Q:

Why the function/macro dichotomy?

Why is the function/macro dichotomy present in Common Lisp?
What are the logical problems in allowing the same name representing both a macro (taking precedence when found in function position in compile/eval) and a function (usable for example with mapcar)?
For example having second defined both as a macro and as a function would allow to use
(setf (second x) 42)

and
(mapcar #'second L)

without having to create any setf trickery.
Of course it's clear that macros can do more than functions and so the analogy cannot be complete (and I don't think of course that every macro shold also be a function) but why forbidding it by making both sharing a single namespace when it could be potentially useful?
I hope I'm not offending anyone, but I don't really find a "Why doing that?" response really pertinent... I'm looking for why this is a bad idea. Imposing an arbitrary limitation because no good use is known is IMO somewhat arrogant (sort of assumes perfect foresight).
Or are there practical problems in allowing it?

A:

Macros and Functions are two very different things:

macros are using source (!!!) code and are generating new source (!!!) code
functions are parameterized blocks of code.

Now we can look at this from several angles, for example:
a) how do we design a language where functions and macros are clearly identifiable and are looking different in our source code, so we (the human) can easily see what is what?
or
b) how do we blend macros and functions in a way that the result is most useful and has the most useful rules controlling its behavior? For the user it should not make a difference to use a macro or a function.
We really need to convince ourselves that b) is the way to go and we would like to use a language where macros and functions usage looks the same and is working according to similar principles. Take ships and cars. They look different, their use case is mostly different, they transport people - should we now make sure that the traffic rules for them are mostly identical, should we make them different or should we design the rules for their special usage?
For functions we have problems like: defining a function, scope of functions, life-time of functions, passing functions around, returning functions, calling functions, shadowing of functions, extension of functions, removing the definition a function, compilation and interpretation of functions, ...
If we would make macros appear mostly similar to functions, we need to address most or all above issues for them.
In your example you mention a SETF form. SETF is a macro that analyses the enclosed form at macro expansion time and generates code for a setter. It has little to do with SECOND being a macro or not. Having SECOND being a macro would not help at all in this situation.
So, what is a problem example?
(defmacro foo (a b)
  (if (and (numberp b) (zerop b))
      a
    `(- ,a ,b)))

(defun bar (x list)
  (mapcar #'foo (list x x x x) '(1 2 3 4)))

Now what should that do? Intuitively it looks easy: map FOO over the lists. But it isn't. When Common Lisp was designed, I would guess, it was not clear what that should do and how it should work. If FOO is a function, then it was clear: Common Lisp took the ideas from Scheme behind lexically scoped first-class functions and integrated it into the language. 
But first-class macros? After the design of Common Lisp a bunch of research went into this problem and investigated it. But at the time of Common Lisp's design, there was no wide-spread use of first-class macros and no experience with design approaches. Common Lisp is standardizing on what was known at the time and what the language users thought necessary to develop (the object-system CLOS is kind of novel, based on earlier experience with similar object-systems) software with. Common Lisp was not designed to have the theoretically most pleasing Lisp dialect - it was designed to have a powerful Lisp which allows the efficient implementation of software.
We could work around this and say, passing macros is not possible. The developer would have to provide a function under the same name, which we pass around.
But then (funcall #'foo 1 2) and (foo 1 2) would invoke different machineries? In the first case the function fooand in the second case we use the macro foo to generate code for us? Really? Do we (as human programmers) want this? I think not - it looks like it makes programming much more complicated. 
From a pragmatic point of view: Macros and the mechanism behind it are already complicated enough that most programmers have difficulties dealing with it in real code. They make debugging and code understanding much harder for a human. On the surface a macro makes code easier to read, but the price is the need to understand the code expansion process and result.
Finding a way to further integrate macros into the language design is not an easy task.
readscheme.org has some pointers to Macro-related research wrt. Scheme: Macros
What about Common Lisp
Common Lisp provides functions which can be first-class (stored, passed around, ...) and lexically scoped naming for them (DEFUN, FLET, LABELS, FUNCTION, LAMBDA).
Common Lisp provides global macros (DEFMACRO) and local macros (MACROLET).
Common Lisp provides global compiler macros (DEFINE-COMPILER-MACRO).
With compiler macros it is possible to have a function or macro for a symbol AND a compiler macro. The Lisp system can decide to prefer the compiler macro over the macro or function. It can also ignore them entirely. This mechanism is mostly used for the user to program specific optimizations. Thus it does not solve any macro related problems, but provides a pragmatic way to program global optimizations.

A:

I think that Common Lisp's two namespaces (functions and values), rather than three (macros, functions, and values), is a historical contingency.
Early Lisps (in the 1960s) represented functions and values in different ways: values as bindings on the runtime stack, and functions as properties attached to symbols in the symbol table. This difference in implementation led to the specification of two namespaces when Common Lisp was standardized in the 1980s. See Richard Gabriel's paper Technical Issues of Separation in Function Cells and Value Cells for an explanation of this decision.
Macros (and their ancestors, FEXPRs, functions which do not evaluate their arguments) were stored in many Lisp implementations in the symbol table, in the same way as functions. It would have been inconvenient for these implementations if a third namespace (for macros) had been specified, and would have caused backwards-compatibility problems for many programs.
See Kent Pitman's paper Special Forms in Lisp for more about the history of FEXPRs, macros and other special forms.
(Note: Kent Pitman's website is not working for me, so I've linked to the papers via archive.org.)

