I can give you a very good reason why you should never be late to church: you miss out on that time when God is glorified. Worship is not a warm-up act; it is effectively prayer set to music. Worship helps prepare our hearts to receive the Word of God.
Worship also can be a powerful witness. I think that when a nonbeliever comes into a setting where Christians are honestly encountering God, it is a testimony, because there is nothing in the world like it. When we worship the Lord, it makes an impression on nonbelievers.
In fact, worship was one of the things that drew me to the little Bible study where I ended up giving my life to Christ. There was a cute girl I was looking for who I knew attended the study. But when I located her, she was sitting on the front lawn of our campus with her Christian friends. I sat down and was amazed at their music. They were simple little choruses back in those days.
Prior to this, I really had been into music. I considered myself a musical connoisseur. I was into the Beatles and Led Zeppelin and Jimi Hendrix and the Doors. But when I listened to those simple worship songs at that Bible study, it moved me deeply. And the reason it moved me was not because of how great they were musically, but because these people were encountering God. And I had never seen anything like it.
So when nonbelievers come to church, they are not just watching what is happening up front. They are watching the people around them. And you are making an impression on them, whether good or bad.
Your worship brings glory to God. And it can be a powerful witness.