If one believes in perseverance of the saints, why "work out your salvation with fear and trembling"? If God chooses, irresistibly, who is saved, then why should we bother with anything? The question I am attempting to articulate and then address is not, "why evangelize?" (ordains means as well as ends), since I expect that answer is relatively well understood. Rather, it is "once I am saved, why bother with sanctification?"
Because you cannot help it. If saved, then being sanctified, that is why it is the evidence of our faith. We come to love God more and more, if we truly love him at all. If we love him, then we will desire to do that which pleases him. What pleases God? Our worship. What is worship? Glorifying God above all else in thought, word, and deed. What is sanctification? Growth in godliness. What is that but becoming more and more like God in those traits where we ought to become like him, such as his holiness and love. That then portrays to the world an image of God clearer than the image seen in others. In other words, in sanctification, we become more like we were created to be, and thus show God to others better, which is worship, as we ascribe what is good in us as not terminating on us, but being an image of the God we serve, indeed, because of the fall and following redemption, we must say that our goodness is not our own righteousness, but God's righteousness counted for us.
Being saved and loving God are inseparable. The hatred of God and love of self is what we are being saved from, and we are being saved to love God, as we were made to, in which we find fullness of life. To continue in sin is to continue as if we still hated God. If we truly love God, then that should be hard, not the default! Certainly, it may involve great amounts of difficulty, but for us who love God, we ought to desire to rather do what it takes to show how much we love God than let it be a secret. If you love someone, you will act like it, unless something is severely wrong. If you love God, you ought to act like it, and acting like it is sanctification.
Certainly, there may be things we wish we could do to show our love for God, but in ourselves cannot. Thus we rely on the power of the Spirit of God in us to work in our lives to cause us to overcome habits and do that which we want to do. We rely on the power of God to work through us to accomplish great works for him. If our salvation is brought about by him, then so is our sanctification. We are not saved and then set afloat, nor even saved then merely guided. We are led by the Spirit of God into the Truth of God that we might thus live as children of God by the power and grace of God.
I am somewhat concerned that the original question might be caused by a misunderstanding about what humans are and what our relation to God is. Sanctification is not a hard toil that we need to be harrassed in order to do. Perhaps we will desire not to put the effort in, but the reminders, the incentive to put the effort in, is that we are in Christ, we are a new creation, our nature has been changed from the sinful nature to the Spiritual nature, so act like it. Yes, it is work, but it is good work, like playing sports is for some, you want to do this kind of work.