It can/would happen to almost anyone. If Obama could run for a third term, his approval would be a lot lower since the attacks would all be aimed at him. I don’t think there’s any Democrat that could get a significant positive approval rating, or any Republican, while they’re running for President, at this moment.
Obama’s approval is actually up, very likely due to the people running making him look good by comparison.
Possibly, but if he was running a campaign, they’d be much lower. Probably not as low as Hillary, since he’s a better politician and campaigner, but probably in the negatives, or even at best.
I agree it’s hard now to be net positive if you’re actually viewed as candidate for President where Obama has the advantage of absolute ineligibility for a third term.
Back to the basic question and considering Republicans, I doubt that relative likelihood as a candidate is the whole reason Kasich for example was polling teens %-points better than Trump v Clinton in the period where those two and Cruz were the remaining candidates (Cruz was IIRC slightly behind Clinton, Trump well behind, Kasich well ahead). Kasich (or Rubio I think) would probably be beating Clinton, though it can be debated how different the universe would have to be for either or them to have won the nomination. I’m not 99.99% sure, but I think it pretty likely.
In part a guy like Kasich polled better because he was ‘generic Republican’ rather than having particular widely disliked personal aspects. But some candidates kind of are ‘generic’. What is there really to dislike about Kasich specifically besides that he’s a Republican and you don’t like Republicans? That’s still enough to lose potentially, but I’d guess not in an election where the Democrat has Hillary Clinton’s specific problems plus general weariness with the party holding the WH for two terms (Bill Clinton averaged a slightly higher Gallup tracking approval in the first half of 2000 than Obama first half of this year, second half is entering the glow of leaving office, but Gore was still pulled down by weariness with the Democrats).