Hopefully they'll see that you deserve it even if it has to go to tribunal for you to get it
Sometimes you have to be persistant, they rely on the disabled not having the energy or inclination to take it further.
PIP is not about whether you can work or not, it's to do with what needs you have day to day. It is ESA that is for people who have disabilities that cause problems with working. They are subtle differences but important ones. Some can have significant care needs and yet be able to work, therefore they would get PIP and not ESA, some people cannot work yet have no significant day to day needs, therefore they would get ESA and not PIP, and some people have significant day to day needs and have difficulty working and therefore should get both. I get both, my ESA also had to consider the fact that I was studying full time, personally I don't think I'm in a position to work even if I wasn't studying. I now have physical issues as well so when my PIP comes up I'll add that in as well, and I should be entitled to the enhanced rate of mobility as well as I really can't walk very far without severe pain and fatigue, I'm so afraid of losing the care component that I don't want to try and get more on the mobility side until its up and will have to be assessed again anyway.