Why does the playwright leave these uncertainties for us? It is concerned with the episode when Willy is abandoned by his two sons in th restarant....

I think that this type of question goes to the heart of
what Miller believes about the modern predicament.  Consider Miller's description of how
he sees Willy:

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[The audience members] were weeping
because the central matrix of this play is ... what most people are up against in their
lives.... they were seeing themselves, not because Willy is a salesman, but the
situation in which he stood and to which he was reacting, and which was reacting against
him, was probably the central situation of contemporary civilization. It is that we are
struggling with forces that are far greater than we can handle, with no equipment to
make anything mean
anything.

It is
the last sentence that might help answer the question.  Willy is set against forces that
are larger than he is and determine so much of his life.  The ultimate uncertainty in
the play is how can we "handle" what is impossible to handle?  There is a great deal of
ambiguity present in the play in terms of who Willy is and the exact circumstances
surrounding him because these are the exact forces are difficult to grasp.  If Miller
wrote a play where everything is answered, where there are no ambiguities, and where
doubt is replaced by totalizing clarity, it takes away from why Willy is the way he is
and why his life is how it is.  The style in which the play unfolds is one where
individuals attempt to make sense of their existence, and in the process, ambiguity and
doubt result.  There has to be a level of uncertainty when we learn about characters
from their own words and without a third person omniscient narrator.  This is logical
because individual bias takes over.  Look at Willy for evidence of this.  We can find
examples where he is blusterous in one scene, and then in the very next one, he is a
shell of a man.  At one point, we see him striving for the stars, and a moment later, he
resembles someone who has grabbed nothing but the sands of the desert.  This change
denies a sense of totality and this makes his character more believable.  If the play
lacked uncertainty, then there would be no questions.  Consider that if all questions
were answered, then Willy would be in no pain because his dreams would have been
accomplished, his kids would have loved him unconditionally, and he would have been an
unquestioned success.  In short, he would have been a success.  The fact that he is not
a success is where these questions arise, and proves Miller's basic idea of why the
audience weeps when they watch this play.  We are not watching Willy as much as we are
seeing our own shortcomings and failures.  We have no clear answers for this,
either.