Godliness. The God-man does not seek this, but it comes anyway because of his/her exemplary life. Look at Mandela or Mohammed Ali or more importantly, look at the life of Christ or Buddha. Millions of followers have given their lives for them and built stupors, temples and churches in their honour.
For them greatness is no match for goodness, but greatness comes anyway because of humanity's need for the values of which they stood. Precisely the reason that we love children. For their purity, simplicity, honesty, sense of oneness ... throw in compassion and forgiveness, although perhaps the child is too young to comprehend this.
Fame, power and influence, not handled properly, lead to the aggrandisement of Ego, greed, self-love, vanity and insecurity, which are all counselled to be avoided, both in the lives of the Christian and Eastern saints alike. Without inner purity and dispassion, it is almost impossible to safely tread this path.