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To repeat: No priest could approach God without offering a sacrifice for himself. Access to God's presence was limited to once a year. The day of atonement had to be repeated yearly.
Let me say this more personally. Even if I were an Israelite in those days, I could not approach God on my own. I would be dependent on a human, sinful, weak, imperfect priest to atone for his own sins before he could atone for mine. Atonement before God's presence would have to be repeated, again, and again, and again, lest I be consumed by my nearness to God's tabernacle.
Reading Leviticus makes the new testament sing.
For Christ has entered, not into holy places made with hands, which are copies of the true things, but into heaven itself, now to appear in the presence of God on our behalf. 25 Nor was it to offer himself repeatedly, as the high priest enters the holy places every year with blood not his own, 26 for then he would have had to suffer repeatedly since the foundation of the world. But as it is, he has appeared once for all at the end of the ages to put away sin by the sacrifice of himself. Heb. 9:24-26
Therefore, brothers, since we have confidence to enter the holy places by the blood of Jesus, 20 by the new and living way that he opened for us through the curtain, that is, through his flesh, 21 and since we have a great priest over the house of God, 22 let us draw near with a true heart in full assurance of faith Heb. 10:19-22
My priest is divine, eternal. I can approach God in Him at any time, anywhere, by faith. His atonement is perfect, final. I will dwell in the unveiled presence of God forever.