Looking at one side of a balanced transmission line is not really very useful on a scope since there is no reference that is meaningful other than the other sid

Looking at one side of a balanced transmission line is not really very useful on a scope since there is no reference that is meaningful other than the other side of the line. Of course there would be lots of noise looking at only one side, since the whole idea of a twisted pair line is to take advantage of common-mode noise rejection at the receiving end. Thinking about things more, you'd need to do the same common mode rejection in the tap in order to not be overwhelmed by line noise, necessitating the use of two pickups per pair. Careful physical design could allow a very sensitive pickup to be designed while canceling noise common to both. However, as you pointed out, low current could make things impossible still. But... the line is driving an inductive coupling in the form of a transformer at the end in order for things to work in normal operation though, so instinctively I think that something could be made to work. As for not being worth it, you are probably right, especially since both approaches could be detected with the proper equipment.