Idon't have a lot of time this morning so my reply will be briefer than I'd like.
It is not about carrots and sticks so much as its about clear signaling of player desire and stakes and game mechanics that will matter to the campaign in question. Without game mechanics, the activity while fun, isn't much of a game. And I'm not talking about having a RP-heavy session; I'm talking about a RP-heavy campaign. When I refer to campaign I generally mean a game that is expected to run for multiple years. As a quick example, no version of D&D offers the DM and other players structured insight into a character's motivations, fears, or desires. Contrast this with Pendragon, FATE, Hero System, GURPS, Gumshoe, Burning Wheel, or Vampire the Masquerade. Almost no version of D&D offers a mechanic for testing resolve of a character PC or NPC preferring to rely entirely on the controlling player's decision. Contrast this with all the above plus the Unisystem and Powered by the Apocalypse rulesets. No version of D&D has mechanics to support social, material, or verbal conflict. Contrast this with Dogs in the Vineyard and FATE.