A Question for Pope Francis

In an interview with an Argentinian newspaper, Pope Francis commented, in answer to a question concerning reported ISIS plans to assassinate him:

“I have said to the Lord: take care of me. But if your will is that I should die or that they do something to me, I ask you one favor: that they don’t hurt me. Because I’m a real scaredy cat when it comes to physical pain.” 

Which is a reasonable enough request, it seems.

But why, then, does the Catholic Church refuse painless deaths to those faced with terminal illnesses?

Update, Mar 12: OK, upon reflection, I realize I'm being a little unfair. The Pope is only asking that he be allowed to die painlessly, something that any of us can do. Whether or not his prayer is granted is another matter.