Your argument stems from a basic misunderstanding of the identity property, so I shall treat it properly.
Although that statement "remains the same" is true, it doesn't disprove an implicit 1. The implicit 1 doesn't change the number, but it is there regardless because, as the identity goes, x/x = 1, ergo 1 * x = x
Even if you say 2 is just 2, it has to be 2 of something. It's a scalar quantity ... it's 2 of 1. That also makes it 1 of 2. 1 is the basic numeric unit ... unity. No other number makes sense without first making sense of 1.
You can't equivocate 1 and other numbers like that; while there is only one 1 of 2 ... 1 of 2 of 1 of 2 is 4. By comparison, there can be an arbitrary string 1 of 1 of 1 of 1 of 1, and it still is 1.
If my implicit 1 is only smoke and mirrors, how do you describe something? What sense does the indefinite article "a" make then?