@Rowenasemolina, you are sadly rather misguided. I teach many many 1-1 sessions, on my own in a room in non-pandemic times with a student giving them an individual music lesson. How we mitigate the risk is by having a timetable where the other music staff know who is where at all times, by having windows in each door so anyone passing can look in and windows on the opposite wall to the door, so anyone passing the outside of the window can look in.
If a kid comes and asks me to explain something, I let a colleague know "I'm just going into room A with X to explain Z. I'll be around 10 minutes." Job done.
I continued to teach live 1-1 lessons in the spring, but don't have the head space right now. They were delivered over Teams and in each lesson, a parent waved to me even though the students were all 14+. When I called a kid in November who had not been in school since March, I asked to see parents; it was actually a lovely thing because they thanked me profusely for getting in touch and they could put a face to the name.
Safeguarding is NOT just about children. It is about the adults too. I'm lucky in that in my current schools, both have given me laptops. One is state of the art and runs Teams. The other is ancient & tries to run Google. In the Google school, because I do specialist work only, I am just covering bubbles at the moment so don't need it. In the first school, I am delivering a live component of each timetabled lesson. I will not use my own device for any of it for safeguarding reasons, safeguarding ME, I use the school-issued machine instead. The only photos on it are those taken with a school device and stored securely on their servers. On my phone, I don't take photos of anything to do with students.
To the OP, I think the Head is trying to safeguard their staff, but not going about it very sensitively. The teacher may well be using their own device - potential safeguarding issue. The teacher may have their own children about - potential safeguarding issue. The teacher may live in a flat/house share where anyone can wander in - potential safeguarding issue. I know these sound extreme, but the Head has to be sure and it is much easier to issue a blanket "no" than go through the whole shebang with every parent.
One thing you could suggest is going into school to meet the teacher after the KW/vulnerable kids have gone home e.g at 4pm for 15 minutes. With you & your DC in a classroom, you could easily be socially distanced. The Head could sit in too so everyone feels comfortable. It's not ideal but I find constructive comments much more likely to yield results.