If you’re renting then you should get housing benefit and if you’re unable to work then you should get ESA (or UC for it all). The PIP motability component is completely separate. I lived for years on housing benefit and ESA without getting DLA/PIP. When I finally qualified for it the extra funds were a huge bonus.
I didn’t get a motability car at first but when my old banger kept failing I succumbed. I couldn’t do without the scheme now and as for APs, I save up and also don’t choose cars with high APs..
PS, I’m a single male who rents his home and generally doesn’t have a pot to pee in but I do have a nice motor car parked outside which I couldn’t live without.