I'm not so sure that grounding really helps. Unless there is a short circuit there should be no current in the ground wire. It should only be connected to neutral at the breaker panel. And if it's not bonded there, you'll have a floating neutral in which everything works, but, for example, the refrigerator can cause intense pain if you touch it in bare feet on a concrete floor. I discovered that the hard way helping friends move into a house that wasn't bonded. I was in a sweat soaked t-shirt and laid down on the tile to remove the bottom hinge bolt on the refrigerator door in order to reverse the door. I screamed like a little girl on a roller coaster! The hot leg was at 50v from ground and the neutral was 70v from ground.
The reason that the ground has no effect, besides not being a current carrier, is that American houses use a split phase system. There is a transformer that drops the voltage from utility levels to 240/120. The xformer has a center tap. From the center to one leg is 120v and from the center to the other leg is 120v that's 180º out of phase with the other leg making the two legs 240v. But all in one transformer.
If you remove the neutral from that center tap, the return from your appliance goes back to the panel on the neutral and, seeing the path of least resistance (neutral to the xformer) isn't available, takes the next lowest path through the other side of the panel, and either right back to the other side of the xformer or through other appliances on that side and back. (Or some combination of both.) That's why some lights get dim and others burn out, the garage door opener goes fast, the microwave gets weak, the TV dies and so on. It just depends on whether the power takes the long or the short route back to the opposite side of the xformer.