Let's first think about the word "speechcraft". in real life there are two uses for speechcraft: informative and persuasive. Well, in a game we don't need to inform other NPC about anything, so persuasion is what's left, and what speechcraft is really about in TES.
Now let's think about why the minigame in oblivion doesn't make sense. In real life, how do you usually persuade someone, especially if the person is a total stranger (or even dislike you for some reason)? You make them like you better. You list facts. You tell them why your suggestion is good for them. You use your knowledge to impress them. You utilize verbal tricks to trick their mind... and so on. However with the minigame, the only factor of persuasion is how much the person likes you (disposition). That's not how persuasion should work, because you can still persuade someone who doesn't like you if your suggestion fits their personal interests.
So, how should we model persuasion in a game where the only way to raise a skill is to use it?
First lets ask ourselves, how do we become better at persuasion in real life? We take classes. We socialize, talk to people. Therefore, we can model this in game as well. I suggest that by doing the following things, our speechcraft skill gets improved:
1. By talking to NPC and exhaust all topics. Intuitively, by talking to people, we learn to read facial expression, we practice verbal skills, and we become savvy with socializing. If we do this, we also encourage people to talk to every NPC.
2. By doing quests in non-violent ways. For some quests you may have a choice whether to kill the person or do it in a peaceful way. By doing that, you learn to persuade.
3. By successfully utilize your other skills in conversations. This is like in New Vegas when you talk to someone and if your science level is high enough you can say some jargon. By doing this you practice using your knowledge.
4. If they combine barter and speechcraft, then by bartering with merchants you can also improve your speechcraft.
This way, the devs still have this speechcraft skill so they don't have to make big changes to the game. They just need to modify the conversation scripts a little bit...
Do you think this can be implemented in Skyrim?