One reason I would guess is the massive fortune that is made off pharmaceutical sales.
If someone takes their life early, that is potentially hundreds of thousands of dollars saved by the family that otherwise would have went to big pharma.
I remember at NY Hospital, this guy (in the next room) was VERY sick (AIDS) - he was at end of life. Had 105+ fever they could not get down. He was laying on a bed of ice, and the nurse was pouring ice water over him - all at the insistence of his sister.
I remember thinking how could she torture her brother so much? I know she loved him. And it was a vain attempt too save his life. He wasn't conscious though most of it, but I think he would've preferred to die in peace and quiet rather then laying on a bed of ice.
He lasted till the morning. What a way to go.
That's why Living Wills and Medical Directives are so important.
The biggest reason may be the irrational terror certain societies have regarding death, which is something easily exploited by terrorists.
Even many of those who claim to know they are going to Heaven when they die are terrified to do so, indicating they don't really believe.
But where does the root of this terror come from? Perhaps it is the false belief of an artificial separation between mankind and nature
IIRC, the doctor in the article discussed how awful she felt at witnessing and being part of these prolonged treatments.
Can't find it now, but this seems to be a topic with a long history on NYT:
https://www.google.com/#q=site:nytimes.com+doctor+prolong+li...
Also:
http://opinionator.blogs.nytimes.com/2014/09/06/when-its-the...