Question

Why should someone get paid by the number of items produced (piecework) instead of the time spent produced?

Answer 1

It takes into matter the efficiency of a worker. If someone can make more items in a shorter amount of time why pay them less than someone who takes longer to make those same amount of items?

Answer 2

Let's say you hire two people to do the exact same job (like cleaning your room).

You pay them $10/hour to clean your room.  The first person comes over and takes 2 hours to clean it.  You pay them $20.

The next weekend, a different person comes over and takes 4 hours to clean your room.  Should you pay them $40 to do the same job that the person last weekend did?

A worker should get paid for productivity, because they will be more likely to be more productive.