Why must trapped air be bled out of a hydraulic brake system after work is done on the brake lines or master cylinder?

1. Air is compressible, so trapped air makes the brake lever feel spongy and reduces braking effectiveness
2. Air improves the brake fluid's boiling point
3. Air bubbles help lubricate the caliper piston
4. Air prevents brake fluid from leaking, so it should always be left in the system