The only reasonable objection which occurs to me is if the installation involves putting unsightly new wires across the building. However so few phone lines need that these days that I think it's more likely to be that the LL just doesn't want the (perceived) hassle of having to have the phone cut off and chase Ts for unpaid bills if they don't organise cut-off and payment themselves when they leave.
I also agree that it sounds as though the LL has misunderstood the request.
'Pause you who read this, and think for a moment of the long chain of iron or gold, of thorns or flowers, that would never have bound you, but for the formation fo the first link on one memorable day'. Charles Dickens, Great Expectations