When a Christian leader is too busy (with writing, speaking, traveling, etc.) to spend time responding to individual correspondence, then that person is too busy. Being a giant in the scholarly realm might work fine for those in secular fields, but if you elevate yourself to the point where the pursuit of knowledge outweighs the personal aspect, you cease to be Christ-like, for he takes time for people.
If through ministry I am ever too busy to do something, I hope that I am too busy talking and fellowshipping with my fellow Christians, to the exclusion of writing, traveling, and so on. God gives life to individuals. The Holy Spirit quickens individuals. Jesus Christ died for individuals. And may we live our lives for individuals.