Since when are ground-based starting devices no longer in common use? Are there any jetliners flying that would still require them?
What was uncommon about the experience in Harare, Zimbabwe that you reference in your question was the arrival of a 747 with an inoperative APU. If I had to bet money, I would bet that they had never had that happen, or if it had, the captain had enough sense to leave an engine running. Harare's ground crew experience was having to start much smaller engines requiring far less pneumatic power from the ground carts. Thus pneumatic carts (huffers) that had had their output degrade over time still had sufficient output to start smaller engines.


  Since when are ground based starting devices no longer in common use? Are there still any jetliners in service that would require them?


As of my retirement in 1999, ground based starting devices were in common but infrequent use. I would suspect that's still true, although hopefully less frequent. Any jetliner engine of size will require a ground pneumatic source to start if the airplane itself cannot supply that with its APU or an already running engine.

Back to my experience in Harare, the first mistake made was that of our dispatch department sending an aircraft there with an inop APU.