Jean, you commented that:
"... But if we want to consider the design activity through its output
(which is, in my understanding, the demand raised by Victor), I think
that most of us will admit that the simple wording of "problem
solving" must be mapped in a new way : most of it would fit under the
somehow generic hat of "sustaining the sales of the company". In such
case, who is everyone ?
If we would restrict ourselves to what happens in a design
consultancy (which is a smaller field), yet, should the "design"
activity include the rethorics (verbal, visual etc.) used to create a
platform with the project stakeholders?
If we restrict ourselves to the steps that run from the preliminary
statement of the problem ("the brief") to the creation of a set of
proposal (the concept, the design), then we might be closer to the
(traditional ?) (implicit ?) definition of the design activity as it
is practiced and tought."

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I think perhaps that these questions can be refined as "where does the
problem boundary lie?" and "who defines the problem boundary?". In the
"smaller field" of design consultancy the problem boundary is usually
drawn fairly tightly and determined largely by the client. Clients
generally have a fairly narrow view of their requirements including such
topics as ease and cost of manufacture, quality, brand recognition,
marketability, etc. Arguably an important contribution the professional
designer makes is to challenge these boundaries to see if there are
alternative solution spaces that can be exploited to generate novel
solutions. Some designers are more challenging than others and some
challenge from outside the client/designer relationship rather than from
within. Working within the client/designer relationship it may be
possible to persuade the client that issues such as usability or health
and safety which can sometimes seem to add to costs are consistent with
goals of marketability and profitability. In time such notions may
become part of established practice and no longer contentious. With
imagination it may be possible to identify new market opportunities for
socially or environmentally responsible products (e.g. clockwork radios,
one laptop per child, domestic solar panels). Challenges from without
occur when it is not easy to convince a client to bear the cost of a
wider social, economic, environmental, cultural, etc benefit. In which
case it may be necessary to bring political pressure to bear to change
market conditions (think Ralph Nader and car safety standards, or more
recently, carbon emission limits).

So I think "whether it would be very valuable for design-as-it-is-
practiced to include the issues of social, economical and cultural
impact in its core." depends on the context, which includes our
personal values and beliefs, the power relationship between the designer
and the client, the likelihood of discovering new design/market
opportunities and wider societal concerns. The context changes all the
time. We are currently seeing millions of Chinese manufactured toys
being withdrawn from sale worldwide because of safety concerns. A
century or so ago issues such as the lead content of children's toys
were not sufficiently high up the social or political agenda to warrant
such actions. Designers can play a part in influencing the context from
within the designer/client relationship and from outside it. I believe
that as designers we have a responsibility to our clients, society and
the planet to be challenging with respect to problem boundary definition
but in order to be successful, challenges need to be appropriate to the
context.
Sorry if this has turned into a bit of a rant.
Stephen