It's actually meant to hang all the way down to the floor so you can pull it if you mess up your transfer. It's common for them to be cut to the height of the toilet so they don't get in the way of cleaning, or because people in charge of maintaining them have no clue what they are for. They are also frequently tied around the grab bars so they are nice and stable and out of the way, and so that if you are on the floor and you pull the cord all it does it rattle the bars up and down and will not trigger the alarm.

In any case it depends on there being some kind of procedure for dealing with the alarm - who is meant to be nearby supervising and responding to the alarm? The cord just flashes a local alarm on the outside the door in this practically deserted corridor! You're not supposed to pull them, you know, they are there because they are in the building code. Like This