PIP award after the Upper Tribunal case (2016) about social support

I am the appointee for my son, who received PIP until he went into mental hospital on April 2020. He is still in mental hospital and hasn't lived in the community since April 2020. Consequently, he hasn't received PIP since April 2020. He has 11 points for his PIP(daily living - not mobility) so receives the standard rate.

I received a letter from the DWP because they wanted to look at whether my son would have qualified (in 2016-2020) for descriptor C in question 9 or whether his award should stay with descriptor B. At the time, when I answered their letter, I didn't receive much advice so I answered that nothing had changed. The DWP wrote back staying that descriptor B would stay then. Afterwards I joined Benefits and Work and read about the effect of the supreme court and decided that he actually did need social support from me, I had understood the meaning of social support better. I decided to send in a mandatory reconsideration letter with more information about my son's condition. I received a reply on 14 Feb stating that the DM decided that the descriptor b was correct.
I'm not sure whether to take this to tribunal as I don't agree with their decision. My son has schizoaffective disorder and has had it the last 10 years. He has delusions of grandeur, paranoid hallucinations (hearing voices) and absolutely not insight into his illness.

The DM stated in her letter to me that at his interview he needed no prompting, seemed relaxed and friendly and answered the questions. However he needed much encouragement, prompting and preparing for him to go the interview. If I hadn't explained t he consequences of not going etc, he would not have gone because he would have felt very uncomfortable. I didn't interrupt the interview because if I had, my son would have become angry. He wanted to give a good impression of himself. Also the DM said he travelled on buses to visit me etc. However he only travelled very rarely and it was the same bus. He went to the depot clinic alone sometimes, and sometimes with me. The DM said that he goes shopping by himself. He does but always to the same shops . He doesn't like to go into shops he doesn't know.
I'm not sure that the support my son needs from me qualifies as social support or just prompting. I am the only one who accompanies him to important events etc, any event that involves meeting people. There is no one else who knows my son so intimately and whom my son trusts. What do you think. Should I appeal his case. I was thinking of asking for a paper appeal as I'm not sure my son will be well enough to come out of the hospital for a tribunal. Or even if he is, he would find it too distressing.