There are other reasons Hill should be a reliever besides his durability issues. He is very effective both in the first time through the opponent's lineup and in high leverage situations. By being a closer (or just a late-inning reliever, for that matter), he would pitch most in those two situations. So, would Hill be more effective as a reliever than as a starter? In a word, yes.
In the first inning he pitches, Hill allows his opponents to hit .236/.297/.279 off of him, as opposed to the .296/.350/.466 opponents hit off of him from inning 2 on. The key to his first inning successed is the fact that he gives up almost nothing more than a single. There have been 33 first inning hits off of Shawn Hill in his short career. Only 4 of these (12%) went for extra bases-3 doubles and a home run. Now compare this to the 36% XBH rate from the second inning on. When a batter faces Hill for the first time in a game (not necessarily in the first inning), they hit .258/.316/.352 off of him. When they face him for the second time, that line skyrockets to .313/.369/.469 and further to .291/.354/.505 for the third (and fourth, fifth, etc.) time they face him. Hill obviously has something special that works the first time through the lineup ridiculously well.
The other main factor needed for a reliever is their success in high-leverage situations (read about the definition here). Hill performed best in the highest leverage situations, allowing a .254/.329/.362 line against. In medium leverage situations, he was decent, with a .288/.336/.434 line against. In low leverage situations, Hill got shellacked, with a .299/.366/.470 line against. So if you want a pitcher who thrives in the situations that make you sweat most, Hill's your guy.
All stats used in this post are provided by Baseball-Reference.com.