I'm not really trying to defend the action of the airline but to give a different perspective.
When a passenger requests wheelchair assistance, like the OP did, it will show up on the ppwk that the flight attendants receives before takeoff. When the plane calls "in-range" of the destination, the crew will let the ground staff know how many wheelchairs the FA has told him are needed. Also, the ground staff can see this info as well with a quick check.
So, let's for example say an arriving flight is requesting 4 wheelchairs. When the flight arrives and the passengers are deplaning, many times a passenger who has not ordered one will just sit down and expect to be helped. Now one of the requests will go unfilled or have to wait. Should the wheelchair pusher have a list of names that requested the service?? Probably, but they don't, at least not anywhere I ever worked.
A request at an origin point is much easier. You request it, it shows up. It can't really be there ahead of time as the agents haven't mastered the art of knowing all the names and requests of passengers before speaking yet. I was working on that but quit in frustration.
