They were in a hurry to pull the plug because the child was an organ donor. They need to get those organs from living people, because once you die, the organs are unusable. So they can only get them from situations where someone is still alive, but comatose/unresponsive.
If he hadn’t been an organ donor, I have no doubt they would have been happy to keep him on life support for as long as the insurance would pay for it.
That’s why I’m not an organ donor.