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Not just the shooter and bullet, but the rifle needs to be able to do its part, too. No dinged crown or other major issue.
A badly dinged bullet tip will lower ballistic coefficient a little, but it's not something you'd really notice much at 300 yards or less. It will also slightly unbalance the bullet, but when Harold Vaughn did his experiment filing bullet tips at 45°, the amount the group opened up was only about half an moa at 100 yards, IIRC. By comparison, a mere 2° angle on the bullet base had several times that much effect. Hence Harry Pope's admonition over a century ago that the base steers the bullet.