Broadcasting & Cable's Michael Malone has the skinny in an article subtitled Syndication or late local news works fine at 11, thanks:
Amidst the speculation that Tonight Show frontman Conan O'Brien might shift to a similar role on Fox, multiple managers at Fox affiliates say they're lukewarm on the idea. All pointed out that it's premature to speculate on an O'Brien-at-Fox arrangement, and none were comfortable commenting on the record for that reason. But their off the record comments indicated a low level of interest in O'Brien airing on their stations.
As noted elsewhere, and in the above B&C article, the timing would be tricky because many affiliates are locked into syndication deals in the 11pm slot, and others have late news programming at 11pm. But the real issue seems to be that the affiliates get more advertising inventory with syndicated or local news programming than they could with a network show.
While I'm pretty sure the FOX affils ultimately don't have as much clout with FOX as NBC affiliates might have wound up having with NBC (where extra political clout was in play due to the Comcast deal still needing regulatory approval) I'll let the affiliates have their day in the sun.
They might never have another one.
Added: Interesting comments from Fox's Kevin Reilly via THR: