Bob, testing is important to gauge the state of the students education. With one on one teaching, where the parent knows the student's educational state, testing is less necessary, or needed rarely, or not at all. Testing has the benefit to allow (might we say force?) the student to relearn material for the test which is supposed to help with material retention. However, we (teachers) know that, if interested in the material, the student will soak it up and if not, will retain little. So, if you are homeschooling and you know your children's educational state, if the testing is burdensome to the curiosity, creativity, and desire to learn, then testing will be counterproductive, and the good that might come from testing (shall we say mostly for the teachers use!) will not outweigh the harm it will do to the child's yearning for learning. There may be times when a student finds testing fun, and for those times, have a merry time at it. When the testing is not fun it is not worth it (assuming we are discussing a one on one teacher student relationship).
One of my students is a homeschooled, self-directed genius. He does not like the word, "testing". So, I call every test a challenge and tell him I don't believe he will ever get 100%. Suddenly, it becomes fun for him.
My other student is not homeschooled and was required to take the SSAT and HSPT high school entrance exams. We used the prep books, and I added my own lesson plans that break everything down.
Also, with him I assigned classic short stories and math problems from Quora.
If I were a classroom teacher, I would test, not for assigning a grade, but to let me know how far a student has progressed. That requires more time, and most teachers don't have that kind of time, which is what makes one-on-one tutoring much better for me. Plus, I could not comply with all the regulations imposed by school districts.
God directed me away from teaching and into tutoring. I thought it was an accident, but something urged me to buy The Tutoring Club in San Jose, CA, and there I found what I was supposed to do.