I had wondered whether that was the case. You're right, it would seem to be peculiar in a lot of circumstances. Can you see Abraham Lincoln's Solicitor General standing up and arguing the cogency of the Fugitive Slave Act to the Supreme Court, with Roger Taney sitting up there on the bench? It would be very odd.
I believe that the Solicitor General was originally created to ward off any resistance to Presidential appropriated powers of the kind put forward by the Lincoln Administration during the war -- suspension of Habeus Corpus, spending money without Congressional approval, etc., and prevent legal challenges to Reconstruction before the US Supreme Court. Maybe I am being too cynical about that.
The only reason I even bring up former Solicitor General Paul Clement here is that I'd read some rumors elsewhere about his reasoning for leaving the post and it was solely in regards to 'DC v. Heller'. He'd been carrying the government's water for years in several cases across various US Circuit Courts under multiple US Attorney Generals and it appears that all that work looks like it might get boned in the ear by the forthcoming ruling out of SCOTUS. As the unofficial 'Tenth Justice', he and his staff certainly have their ear closer to the rail than anyone else outside of the Supreme Court on which way the wind blows for Heller.
Clement actually served as US Attorney General for a 24-hour period during the transition between the outgoing Gonzales and in the incoming Mukasey, and that's the best he'll ever get considering that even if McCain wins there would be a significant outcry from RKBA advocates if Clement were to be nominated to the Supreme Court or tapped for US Attorney General. Liberals hate him to pieces for arguing against supposed rights of Guantanamo detainees and for defending Donald Rumsfeld in Hamdi v. Rumsfeld and Rumsfeld v. Padilla.
It simply could be that all his labor got him was to be reviled as an un-Constititional creep and that his career in government was at an end. The US Supreme Court hasn't seen the last of him, though. He'll have a rewarding career arguing before them at various times, I'm sure.
He's now a professor at Georgetown University Law Center.