I can definitely see your point, Hidden. I think the reason why Jeff doesn't work 100% as a heel, is because the fans are torn (about whether to boo, or cheer for him).
I can't help but think about when WCW tried to turn Sting heel, towards the end of their run. I can't remember the exact dates, but it must have been late 1999ish? WCW creative gave him heel-storylines, but the fans wanted to cheer for him no matter what he tried to do. Sting wasn't really trying as hard as he could have to be booed though...besides, how could you really boo Sting at the time? He arguably had the coolest entrance in all of wrestling (at least at the time)...the lights would go out, and "Seek & Destroy" by Metallica played while simulated thunder & lightning went off in the arena. I can't remember for sure, but I think Sting was still coming down from the rafters on the zip-line, too (or did they nix that all-together after Owen's tragic death?). The fans loved Sting at the time, no matter what creative tried.
Similarly, AJ Styles had a hard time getting over as a heel when he was paired with Ric Flair last year. He definitely got better as a heel as time went on, but AJ's moveset ALONE makes the fans want to cheer him.
I'm sure there are other wrestlers from the past that fell into this category, but I can't think of any more off the top of my head. I'm pretty sure that some other posters will be able to come up with some more?
I think Jeff has a similar "hard time" getting over as a heel, because his character and moveset makes the fans want to cheer him. In my opinion, I think Hardy is doing a better job of playing a "bad-guy wrestler" (as Andy Kaufman would have said) than AJ or Sting did in these situations.
I do understand your gripe though, I really do. I think most of the TNA roster (a lot of WWE's too, for that matter) would benefit from some simple acting lessons. I'm actually surprised that these companies don't make it MANDATORY for their wrestlers to take some classes. I seriously think that would really help a lot of the current roster, ESPECIALLY Jeff Hardy. If nothing else, they should be working with a coach that would help them become better public speakers.
Acting and/or public speaking SHOULD be a huge priority for all wrestlers, obviously that kind of thing counts for a lot when it comes to how over a wrestler is (or can become). Maybe the wrestlers are required to take some of these classes? ...I dunno.
If I was working for TNA and/or WWE, one of my first "acts" would be to hire at least one acting coach that could help develop characters.