Yes, abandoned wiring should be removed, or safed-off, tagged and secured, PERIOD.
In this area, "low voltage" cabling has been a thorn in a lot of comm buildings. "Line" voltage cabling has not been too bad.
Although "removal" is not code required, the clients that I represent have made it a "SPECIFICATION" in all renovation projects. Conformance to the "spec" is assured by a owner's rep doing a follow-up physical inspection in addition to the local AHJ.
Basically, cleaning up "past sins" makes the whole job neater and easier to work.
Personally, I feel that it should be inclusive into the Code (NEC) that unused, abandoned wiring & conduits be removed or tagged, safes-off, and secured for future use. (IF the cable/wiring is in re-usable condition)