It's also misleading to treat it just like another independent private company too (not just because Motability consists of both a limited company and a charity (or two, IIRC)). The limited company reinvests revenues or transfers to its charity, not to private shareholders. Its origin was a charity.

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