I’m a HCP specialising in this area. Helmets don’t work (see link to research by pp). Physio is helpful if torticolis is present. The NHS used to pay for them, until the evidence showed that they are ineffective (approx 20 years ago) so nothing to do with cost
Sorry, but if you are a HCP you should understand that there is a very poor evidence base. The one paper cited here is full of holes, the main one being that you can't blind people to whether they are in the control (no intervention arm) or the intervention (helmet) arm. This will always be the case with these type of trials as they are not like a pill where you can hide the placebo/intervention. This means that the non-intervention group may have been alerted to their being a problem just by taking part in the study, done some intervention (e.g. more tummy time), thereby increasing the chance of a null result. The two groups were also not the same with the same problem.
Like lots of health problems, you have to take a guess, reading the very slight evidence, about whether your personal child will benefit. On average, there was no difference, but what that means is some got better, some didn't and that wasn't drastically different whether they wore a helmet or not. Many of the children did grow out of it, but actually most did not and that's what the paper itself states.
I would agree with the HCP that getting physio intervention is a must in this situation whether or not you go ahead with the helmet.
Finally, the NHS did not pay for private helmets 20 years ago, they used to make a really crappy one in Bristol around that time, or slightly later, until it was abandoned as far inferior to the commercial products. They certainly didn't pay for private treatment when I was in the system, and they are very unlikely to, as the evidence-base simply isn't there, one way or the other. One paper or even two RCTs wouldn't be enough, esp with the design flaws of the BMJ one.
This American Academy of Paediatrics review shows what evidence there is and concludes there isn't enough:
www.aappublications.org/news/2016/10/27/Plagiocephaly102016