Why Do We Always Teach It This Way

I wondered why we always teach students to distribute first when teaching them to solve a problem like the one to the left.  I know we teach it that way even for a problem like 2(10  + 3).  We have the students go through the same process of 2 *10 + 2*3 = 20 + 6 = 26.

My students often wonder why they have to carry out the process with integers.  I know it's used to help them learn the process but for most of us, its easier to multiply 2 * 13 rather than break things up.

I read an article that sounded like a cool way to solve the same type of problem.  Since there is only one variable, the other methods states one should divide first as long as the answer is divisible by the number in front of the parenthesis.

It saves a step and is much easier.  The article said one should use the distributive property if you have more than the one variable and will need to combine like terms.

I'd love some feedback from readers on this.   Do we have to teach students to always distribute or is it possible to teach them to learn to differentiate two different cases so they only distribute under certain circumstances?