I did this, years ago, when there were no companies operating in the UK and I had to get a specialist from Germany to help. My dd's face was quite badly affected though, it wasn't a small patch at the back, her ear on one side was 1 inch in front of the ear on the other side, and her face looked like it had been smacked by a frying pan (i.e. parallel flatness).
I decided not to worry what others (including the HV thought) and go ahead, we did, she has a perfectly symmetrical head and is very lovely looking. I am not going to out myself, but saying 'the hair will cover it' is not always true- what if the child has short hair, or loses their hair?
She did also have torticollis though (which the helmet consultant demonstrated), so we did neck exercises for that.
The good thing to come out of all this was my second started to develop a bit of a flat patch, like probably 50% of babies, and so I immediately did lots of tummy time, carried her, repositioned her in the cot so she would look out both ways, and once she was sitting, it was gone by about 9 months. So in mild cases, and without any neck disorder, I think it's perfectly possible to reposition babies and this just disappears of its own accord.
I knew my older's wouldn't just disappear though, and I have no regrets any more than I regret her having block braces for 2 years!
It is cosmetic in the vast majority of cases though and I think there's little argument the NHS should be starting to pour money in, however this leaves the current state of affairs as very unfair to those who don't have the money, as treatment is expensive.
We only got laughed at once, by some teenagers. Most people smiled at my little girl in her pretty helmet (they weren't patterned then and I stuck butterflies all over it) and it was all done and dusted very quickly.