You're not alone. But the team still was comfortable enough with the idea to ask the player if he would do it, according to the New York Daily News. Why would they do such a thing.
There's an argument to be made for Pelfrey in the role. Perhaps if he concentrated on just his split-finger and two fastballs, he could be more successful in shorter stints. Or. Maybe going to the bullpen could bump his fastball velocity over 93 MPH and make the rest of his pitches more effective. We know that moving to the bullpen gives you .7 MPH and 17% more strikeouts from past research. Give Pelfrey those things and he'd be better.
But there are plenty of reasons why it's good news that Sandy Alderson vetoed the move eventually. One of the simplest is platoon splits. You need your closer to be able to get out batters of both hands, and Pelfrey's arsenal does not provide for that. Pelfrey has a 4.80 FIP (4.71 K/9, 3.75 BB/9, 42.8 GB%) against lefties and a 3.86 FIP (5.47 K/9, 2.62 BB/9, 54.9 GB%) against right-handers. And his pitches have platoon splits that suggest this sort of thing is predictable.
Beyond that, there's the fact that Mike Pelfrey does not have the swinging strikes to be a closer. He's getting whiffs on 5.6% of his pitches, which is far short of the average (8.6%). Chris Perez is the only (qualified) closer who has a worse whiff rate. Jason Isringhausen (7.3%) gets more whiffs. Kevin Gregg (6.3%) is closest. Yeah, give Pelfrey a few more whiffs in shorter outings and he'd still be among the worst in the business (at best he'd graduate to Jon Rauch and Sergio Mitre territory (6.7% each)).
Just because Pelfrey would be better as a reliever is not a good reason to make him closer. Just because he'd get a few ticks back, doesn't make him a good stopper. Pelfrey doesn't have the pitches or the whiffs to be a good closer. He's an asset, as a starter, while he's cheap.
And even if he transitioned well and was just as good as Bobby Parnell, which is actually doubtful, he has fewer years of control left than Captain Fastball. Moving Pelfrey to closer just doesn't make sense.