Same reason that big cities have an ambulance, really.
We saw that every house seemed to have a medikit, but we also saw that Elysium had industrial sections designed for humans.

Also, since Elysium doesn't seem to have any way to destroy near objects aside from calling up someone on the ground and telling them to get the Javelin Mk. XVI out, they probably need those med ships in case of a meteorite impact. =)

Niell missed an opportunity to establish the med ships presence when Carlyle was shot down. One of them could have been dispatched to give him emergency medical treatment, but then be recalled when it couldn't get to him on time.

: The whole reason people were trying to get there
: was the beds. Why not send a few to earth? Wouldn't that stop the people
: from trying to get there? I mean, charge all the people on earth $10 each
: to use them and you'd rake in billions.

The ending to the movie was laughable. You have, what, three ambulances to treat the billions of people in need of medical attention? And the, ah, the billions of people who are going to fall ill while you treat those? And the medical records of the worldwide shantytown are not only good enough to form a plan of treatment, but those records were already hooked into the Elysium mainframe?