Yes, yes, and yes again!
I will caveat that you need to hit on the RIGHT private tutor; he or she needs to jive with your kid, but that's not usually a monumental task. Part of being a private instructor is being able to quickly pivot personality and learning style to best suit the student's needs.
Delivering confidence to kids is one of my favorite things; so often I get "I hate school" students who really just find themselves lost and frustrated. They don't hate school, they hate that feeling of being left behind and confused.
Teachers have a lot of students; they have a lot of pressure and so, so much work to do. A private tutor can slow things down, can find the holes in education and plug them in. In turn, they give confidence back to the student -- it's not that your child hates school, it's just a wrong turn somewhere and we need to course correct.
Working one on one also allows us to delve into topics that are more interesting for the student. For example, if I have a kid who hates math, I don't spend the entire time harping on sets of formulae. As a private instructor, I have the luxury to develop a course that hits on his hobbies. Let's say video games. Easy! Let's explore how math is used in gaming -- how designers need to adhere to physics (which is math!) or how you unconsciously use math to calculate resources during gameplay.
I find common ground and get to use it to find a reason for a student to think positively about something she may have found hard. One on one, private tutoring, pulls some of that performative pressure off the student and lets him or her shine.