Hmmm...in regards to assitance being provided by airports centrally rather than airlines themselves, i'm sure it'll work for airlines that use agency staff, but my airline has it's own wheelchair assistants and i think they are by far the best in the airport.
Agency staff in my view are never a good substitute for a company's own employees. It's also easier for us to chase up keep tabs on passengers who need assistance as we can easily get into contact with out own agents rather than having to contact some central agency.
My airline also doesn't charge for this service BUT! IMHO I think unless you can prove you are registered disabled it should NOT be free. Everyone else should pay because believe it or not there are lazy pax out there who know they skip queues and etc when using this service, and this would weed them out.
It's also interesting that older pax from certain cultures NEVER want wheelchairs no matter how old or how far away a gate it, yet for some flights there will be 20+ wheelchairs for elderly pax, stretching agents to the limit and diluting the service offered to other pax on othe flights leaving.