Anth. I must send you my KML file... (just like the Terminator, I have "detailed files".)
The line you refer to is actually used for a single purpose, namely hauling the stuff that the citizens of Edinburgh throw away out to East Lothian, to be dumped in a hole.
Train runs most days I think, called the "binliner" in spotter terms. The line terminates at a siding by the Powderhall refuse depot (see rows of big CEC containers on flatbed wagons there). The unsurfaced bit of path from "fiveways" junction meets there in the security fence. Until the early 80s the line ran all the way to Granton via Trinity path as there was - amongst other things - a Texaco oil depot that generated enough traffic to keep it going.
As to what they did (or didn't) do with the rest of the "Abbeyhill triangle" there, good point.
Also, the existing line (continues under Marionville Road, Easter Road, Leith Walk) is single line on a former double line trackbed, would be plenty of space for running a cycle lane alongside it.
The Southern & Southside Junction Line ("sub") is fairly heavily used as a freight only and diversionary toute. Just not for (stopping) passenger services, so there's little scope for putting a cycle lane on it!
There is traffic most days along the line into Leith Docks, mainly hauling imported coal out or sections of pipe in. Of course nothing like its heyday, but more than there was even 10 years ago.