The Daily Grind: should PvP rewards give PvE benefits?

Not everyone likes PvP. We're fine with that. De gustibus non est disputandum, as the Romans used to say: don't argue over tastes. But what happens when a game's designers need to assess motives for PvPing, and allocate it some sort of reward? Should they make PvP rewards useful for PvP and nothing else, ensuring that players who don't want to PvP won't feel left out, or should they encourage PvP by giving PvE benefits to PvP rewards?

As a sort-of example, we ran a feature on the PvP minigames in City of Heroes. Although you don't have to defeat any other players to get those rewards, you do have to enter PvP zones and risk being beaten senseless. Two rewards in particular, the Shivan and the Nuke, are highly useful in PvE. What's worse for non-PvPers is that the PvP zones contain badges, one of which is required for a Villain accolade (a special mega-badge that grants a power not available otherwise). Age of Conan is also on the verge of incorporating PvP XP and PvP gear, though it remains to be seen how the gear will compete with what's already available. So far as we can tell, it will look a lot better, at least.

Do you PvP? Should PvP-linked rewards only ever be useful in a PvP context, or should they have PvE applications too? Are non-PvPers justified in complaining if PvP activity gives PvE rewards, or should designers not try to make everything for PvE available to everyone, regardless of preference?