Is the word "single" necessary to be added when specifying a thing?

I think the word single is not necessary because the article a or an has done the job.

So the phrase "a single object" should be simplified as "an object". What do you think?

You are definitely right. Indefinite articles can be used only before single countable objects, therefore your assumption is right. It would be:

an apple = for any single apple
the apple = for specific single apple
the apples = for 2 or more apples

It would never be:

an apple = for 2 or more apples
an apples = for 2 or more apples

Your assumption is right and would create an unambiguous statement.

Single is there to put the emphasis on the fact that you are requesting a single object, not more. Imagine the following:

Daughter: I don't get it. When I bake the pie, it's never as good as when you do it.
Mother: Try adding an apple.

Even though in the above conversation the mother grammatically tells her daughter to add one apple, the apple may easily by understood as "a fruit", not "an object", and then the daughter may not know how many apples is she supposed to add and ultimately, she may add more than one.

If the mother said, try adding a single apple, it would be understood as "not more than 1 apple".

"Single" is just added for emphasis I think.
For example:

John didn't even give me one single dollar.

If the speaker had said "one dollar", it wouldn't have been as "strong" as when there was "single".

It's true the "a" and the "an" specify that the subject is singular, but "single" is for emphasis.