Bike chain teeth do not have straight sides or a convolute profile. They are wedges that act as ramps for the rollers. As the chain wears, it is no longer possible for the rollers to all sit at the base of the teeth. Instead, to account for the increased pin-pin distance, they begin to ride 'up' the teeth at the point of first engagement. You can easily see this when looking at a worn cassette used with a stretched chain. The tooth profiles become sharply hooked as the roller wear works in from the 'side' of the tooth.
https://pbs.twimg.com/media/EFYuxlJXYAA89-b.jpg Note that the lowest point of the profile remains at the original base of the tooth, and then is angled up.
In a worn chain, the rollers engage high up, and then work their way down (under high load) until seated at the base. In the unworn condition, engagement begins at the base of the tooth where the forces are better spread over the roller.
In point of fact, the forces are spread out over more teeth when worn. The first tooth engagement might begin 3mm high, then 2.5mm, then 2mm, etc. over ~6 teeth. Whereas the fresh chain might manage 2 or 3. But the wear and friction of the worn chain is much higher as you have a great deal of motion under high load as the loaded rollers creep down. The unworn chain has perhaps higher loads, but the roller is essentially seated and immobile at the base of the gear for this.