I'm a primary tutor and went 100% online in March. Didn't lose a single client and lots of people booked extra. It worked brilliantly and everyone was very happy with what they were getting for their money. They all had the choice to leave and didn't.
Since September I've been offering a choice of online and in person with the understanding that we may have to move back to online. Only 6 out of my 21 students have come back in person to my offices and the rest have chosen to stay online so it clearly works very well for them.
It tends to be people whose school's online provision was dire who are anti online tuition, or those who have never actually tried it and make assumptions. It's a personal choice of course and some children may struggle with the technology but in my opinion the quality of tuition is down to choosing a decent tutor who is invested in providing excellent lessons, not the method of delivery.
The main issue some people seem to have is thinking that their child won't possibly be able to concentrate for an online session but this would be the same for in person in my opinion (possibly some exceptions for SEND). A decent teacher will ensure the child knows how to use the technology and they'll make the lesson engaging and interesting.
My daughter is 15 and has two carefully chosen online tutors every week. They are worth every penny and she's making excellent progress. I love the fact that I don't have to take her anywhere or have someone else in the house.
So, personal choice I guess but it can work brilliantly and has many advantages over face to face, especially at the moment.