I will admit that there is one type of worksheet that I used in the past and found relatively beneficial, although it had a different kind of flaw. For my Basic Math, Pre_Algebra, and Algebra classes, I had several books of "self_checking" worksheets. These worksheets had puns or puzzle questions at the top, and as the students worked the problems they were given some kind of code for choosing a letter to match that answer. If they worked the problems correctly, the letters eventually answered the pun or riddle. Students enjoyed these worksheets, but there are a couple problem areas even with these worksheets. Some students would get the answer to the riddle early and then work backward from letter to problem answer, so they weren't learning or practicing anything.
There are some new materials being developed now based on what we are learning about how the brain learns. These brain_friendly materials should be an improvement over what has existed. I recently bought a book by Marcia L. Tate titled "Mathematics Worksheets Don't Grow Dendrites." I highly recommend her book. She gives a great deal of information on alternative activities that are better for your child's brain development and for learning.