Yes people should be allowed to choose someone who can speak for them when they are ill because if you want your wishes to be followed you would want someone to voice that to the care takers so that way if you are to pass away no one would feel bad about it , it's your life your choice.
When people fall gravely ill, it can make it extremely difficult for them to conduct business, or handle personal matters of importance. Sometimes, it can make it impossible. People need to be able to legally allow someone else to speak for them in these matters. That way, matters that they need to take care of, do not go unresolved.
Seriously, who else is going to do it for them? Obviously, the person they pick must know how to communicate with them when they are in that state. The person they pick must also know what they want when they are in to much pain. The ill person trusted them enough to put them in that spot. Who are we to decide otherwise?
If people anticipate a situation in which they'll be unable to speak for themselves, they have the right to delegate someone else to speak for them. This is the same principle as "power of attorney," by which you can authorize someone to make legal decisions on your behalf. That's an established practice in law, and so is making a living will, which states what you want done if your quality of life is irreparably damaged. With those precedents in mind, there is no reason why people shouldn't be allowed to choose someone to speak for them when they're gravely ill.
Yes, they need to be able to let someone choose for them whether they want to live or not when they are so ill that it is apparent that they are on their death bed. If there is a chance to bring them back though, they need to try to.