People use the mobility part of their PIP payments to lease a car from Motability which is an independent company, they could use the mobility payment to pay for taxi instead.
But the only reason it exists is because of government funds and government policy.
The scheme would collapse if the government stopped allowing benefit money to be used for Motability leases. The banks lent them money under the reassurance of the government funding.
But yes, they lease the vehicles, they don't sell them.
EDIT: my comment may have some minor inaccuracies. I just found https://publications.parliament.uk/pa/cm201719/cmselect/cmwo... - a very detailed description of the company, charities etc
It’s not independent, because it derives all of its income from the government and uses it to buy people brand new top of the range cars.
You're gonna have to cite sources on that one, but I would sincerely doubt that £77 a week will allow you to lease an Audi.
Also the pip claimant has to be probed by a panel every three years to keep getting the benefit, unlike say a state pension (but I paid for that I mean possibly you did, its still a non means tested benefit, unlike PIP)