The purpose is to stop economically meaningless queue-jumping. Without it, anyone could step in front of a resting bid for a hundredth of a cent and take the whole queue, destroying the incentive to display size at all.
The rule constrains displayed quotes, not all executions. Off-exchange fills and midpoint crosses may still land at sub-penny prices, which is exactly how retail price-improvement of a few hundredths of a cent is generated.
Example: you may not post a bid at 25.0001 to jump a 25.00 queue. But a wholesaler may fill your buy order at 24.9997 against a 25.00 offer, delivering 0.03 cents of improvement — on 200 shares, six hundredths of a dollar.
Related: minimum-price-increment, price-improvement, reg-nms, wholesaler