I hope and wish you well that you don't have to stuck with this namecheck. As you have no idea how frustating this could be.
There are many reasons why some one woudl want to have a GC in hand asap other than being eligiable to work. Including but not limilting to ,one doesn't require a visit visa for certain countries. Plus ppl have their immediate family members(parents, childrens etc) overseas, who they want to sponsor as soon as they can, after they get Naturailzed, but first they have to cross this obstacles of getting their namechecks cleared. And not everyone has clean immigration history, so if they have ever overstayed their visas than they can't leave country w/out a GC.
A/c to my research in 80-90% cases Sueing is the only method which seems to work, otherwise USCIS simply doesn't care at all. If you don;t sue them you can be waiting for rest of your your life easily or atleast for several yrs w/out hearing a single word back from them.
Thanks