Some aircraft (but by no means all) are no doubt equipped for mobile phone service, but as far as I am aware, a mobile phone, suitable to the area of operations is not yet a required item for flight crew.
Particularly on the Helsinki flight, they would have had to shuffle sim cards and service providers to call the number, and it is by no means certain that mobile phones are a reliable form of emergency communication.
Or have I been out of touch too long?
A crew on a U.S. carrier would almost certainly have immediate access to cell phone communication while taxiing in to JFK from an international flight in my experience.
Sometimes the access is a little too immediate, I've had coworkers texting and checking voicemail before I can stow the spoilers when exiting the runway.
The AA captain had a lot on his mind no doubt and it is the case in the U.S. system that the captain is often one of the last to be informed when there is a deviation from the original plan of operation (don't ask me how I know
).
The tower was probably just trying to be discreet by asking for a phone call. Unlike with the old analog AMPS system, modern digital cellphone transmissions are extremely hard to monitor without cooperation from the service provider from what I can see.