I'm curious-how is Nero's story illogical?
He lost his entire world and seeks revenge on the person who promised to save it. At some point in time, the mind is going to snap under the strain and there can be a break with reality, where no rational explanation is going to satisfy the loss.
Maybe it is illogical, because Nero isn't rational. He is psychotic, in the most clinical of ways, due to his loss. To me, that is the most tragic of backstories and all the more fascinating.
These are separate, but related issues.
The idea of witnessing the destruction of your home planet is, certainly, enough to drive an already unstable mind insane. However, his crew should be able to recognise the completely irrational nature of his quest for revenge.
He, incorrectly, blames the Vulcans (and the Federation) for the death of his wife. He should blame the Romulan government which, apparently, didn't take any steps to ensure that Romulus was evacuated before it became inhospitable (either destroyed by its sun or destroyed by a black-hole; the only two possible outcomes).
He, then, incorrectly, comes to the conclusion that the Vulcans from a reality where the Supernova has not yet even taken place, are
just as blame-worthy as those who, in his reality, he blames (
incorrectly) for the death of his planet.
He (and his crew), then, has over a decade to think about exactly whether or not he's being entirely rational and, incorrectly, chooses to go ahead with his plan anyway.
I could buy that he was just a psychotic thug, but it still wouldn't explain why his crew don't come to the same conclusion.