Members of the Christian religion are under the impression that there is a desperate need to save sinners from everlasting punishment for their sins. Of course, religionless Christians are well aware that God already took care of all that through Christ some millennia ago, and that nobody will be punished forever. But if everybody has been (or will be) saved from death, what is the point of evangelism?
As much as we’d love to see everyone enjoy eonian life (a better translation of the Greek term that religious Christians translate as “eternal life”), we also know that only those God has elected for it will. But those who have been elected still need to hear that Christ died for the sins of the world and saved them. In order to believe this good news (aka Evangel, which is where the word “evangelism” comes from), they do first need to hear it. We don’t know who God has predestined for eonian life, so we preach the Gospel to everyone, not so they’ll be saved from the mythical fires of hell if they’re smart enough to choose to stop sinning and ask Jesus to save them (this is the false gospel of works that the Christian religion preaches), but so the chosen few can hear that they have already been saved and be given the faith to believe it (faith is a gift from God; a gift He doesn’t give to everyone, but rather to the few He elected to be members of the body of Christ).
When the last chosen member of the body of Christ is brought in, this dispensation will finally come to an end and we can move on to the next. So a major reason we proclaim the Good News is the hope that we’re speaking to the last member of the body of Christ and can finally leave this dark age behind and move on to better things. In some ways you could say that we preach the Gospel, not to save sinners from hell (which doesn’t exist anyway, at least not as most people understand it), but to save ourselves from this fallen world (eschatologically speaking, of course).