When these things come up, sometimes I go to SO to see if if I can find analogous situations. Then I try to think of a justification.
Program, code, coding. This may be a larger question of, "Do we want to hunt down and kill redundant tags, or are some tags almost necessary because they represent a massive subsection of questions?"
(trying to play devil's advocate here) It might be useful to divide all SO questions into at least one major category: coding, scripting, version-control, etc. Which could imply that SF questions should always belong to either server mgmt, desktop mgmt, network mgmt, documentation (applies to both), etc.
I suppose that would make me lean more toward a merge than eradication. Sysadmin is such a loaded and nonspecific term, I'd probably synonym it to system-administration, which is at least a (possibly) manageable definition. Provided we could all someday agree on whether a "system" is a desktop and/or server and/or network and/or any "group of independent but interrelated elements comprising a unified whole".
This is where the SO analogies break down. It feels like they actually have more self-defining terms upon which they can agree (a statement I'll guess they'd find pretty humorous).