About three years ago in Colorado Springs, three drunk teenagers broke into the home of a 93 year old man and his wife. The teenagers were all swinging baseball bats and tire irons. The 93 year old male pulled out a Colt .45 ACP fired one warning shot and then drilled the first kid in the chest, one-shot. Great. The other two advanced, and hit his arm with the bat. At that point, his aim was no longer ideal. He took four more shots to get one in the arm of the attacker, then a second round that disabled him. At this point the third attacker fled, and he fired one more shot that grazed the buttocks of the third attacker. Police, called by the wife at the start of the attack, took 4 minutes to arrive. They followed the blood drops to the third attacker who was arrested.
Total rounds fired: 8
Rounds remaining: 2 or 3 (not sure if he had a chamber + 10, or just the 10 in the mag)
Had the third attacker continued to press, he would have had a chance to drop them. The three attackers were later linked to another home invasion where they had beaten an 80+ year old couple to death after repeatedly raping the wife. Your three round limit would have ensured two more dead victims, and only one dead attacker.
If you limit weapons to three rounds, all you ensure is that home-invasion teams will start having at least four members.