why do they only allow them on 28?
That is the only runway that has been certified by the FAA for CAT II approaches. See here for the approach plate:
http://www.myairplane.com/databases/approach/pdfs/00411I28C2.PDFI don't know all the specifics since I am a GA pilot authorized to only fly a CAT I ILS approach (ILS with standard 200 & 1/2 mile minimums), but I would surmise that approach lighting, quality and angle of the ILS signal in that direction, missed approach options and perhaps even cost to certify runways for lower approaches all play a role in determining what runways receive certification for CAT II/III approaches. Even the larger airports like Boston, LAX, and Chicago have a smaller subset of their total runways certified for these types of approaches.
Note: I made a mistake regarding CAT III approaches at SYR. I now see that runway 28 only goes down to a CAT II approach, which has a lower minimum ceiling and visibility than the standard ILS but not a 0/0 minimum of a CAT III. I wonder if something changed at SYR to lose their CAT III certification? Hmm... I'll need to ask around about that.