They also lived at a time when the newly formed movement (christianity) was under significant persecution, so it is not at all surprising that they considered membership of that movement (as defined by belief in Jesus etc) to be more important than almost anything thus the emphasis they believed would be placed on belief within eternal judgement, because it was for that they were were suffering hardship while they lived.
As for the nature of the judgement... well we are talking about an 'afterlife' a state which comes after this temporary life.... it would not be 'solved' by positing a temporary outcome, so it makes sense they would claim an eternal one (else there would be an after-afterlife etc) and because the evaluation criteria (belief) easily conforms to group membership, it is easily seen as Us vs Them, in those conditions it is obvious that 'Us' are going to be considered worthy of a pleasant experience, while 'Them' considered unworthy of a pleasant experience - instead an unpleasant one.