does a general curve which specifies aging in function of junction temperature exist?
Not directly, no. It really depends on how you define / measure "aging", and on what specific PN junction you're looking at:
Is its existence feasible, or there are too many variables involved not allowing to define it?
The exponential function usually cited essentially describes the speed at which (unwanted) chemical reactions happens. That happens to have something to do with how likely it is that certain impulse or position space pertubations occur – and that's an exponential function of temperature, in general. Sadly, reality isn't that easy, because, as you'll notice, a junction at 540 K isn't just "much faster aging" than a junction at 270 K, it's probably instantly broken, since probabilities that you could neglect (like simultaneous disintegration of the crystal lattice in very many places) suddenly become likely.
Also, external factors influence the likelihood of you undergoing damage than just the temperature of the junction: For example, temperature of a bridge rectifier under load will undergo variations, and if you look at these, you'll notice that for a given load you don't get the exact same temperature every time – you get something that has variance. (That's because a) you can't measure anything without variance, that's how physics is, and b) well, environment temperature, wind, position, thermal resistance of wire, dust, …)
And with that variance, you get a probability that "something with a probability that very overproportionally increases with temperature" and immediate failure modes become vastly more likely. And so, component aging is a multi-causal thing that can only in very complex models be related to temperature.
And why is not common to include such information in the datasheet?
Because you typically find something like a mean time between failure in there, if you pay for that qualification. Semiconductor producers might be a bit reluctant to publish data that allows the competition to make conclusions on their doting processes – and a diffusion speed vs temperature curve would most definitely.