The problem is dealers don’t get much profit from organising Motability cars. The ones I have met, often say the paperwork and hoops to jump through are not worth the reward and they have to do it because their Manufacturer makes it a condition.
Whether it has changed now but Motability also had a policy of their own service intervals rather than the manufacturers. Hence dealers often missed out on gaining the full service costs plus they are not allowed to replace the tyres as this has to be Kwik fit – so more opportunities lost.