It's worth noting that, for example, the metallic wire conduits and water pipes in your house are grounded, so it's by no means obvious what the lowest-resistance path to ground might be. The housing of my toaster oven is made of metal, so what's the closest path to ground? The faucet? The refrigerator? My cabinet handles? The metallic body of my conventional oven which is a few feet away?
Imagine a fault occurring in some appliance that you're touching, and ask yourself how certain you are that there is absolutely nothing nearby which is connected to a pipe or a conduit or a large appliance or wet soil or [.....]. Are you sure enough to risk your life or your families lives, when the alternative is to add one extra wire to the appliance which would save you in the event of a (even highly unlikely) mistake?
As a toy$^\ddagger$ example, imagine that somehow a fault develops in your ungrounded dishwasher which connects the nice, aesthetically-pleasing brushed steel panel on the front of the appliance to the hot supply wire connected to the outlet under the sink. If you're standing next to the dishwasher and not touching anything, then your resistance to ground is probably quite high, so you should be safe even if you grab the electrified handle. But that's not how people use their appliances at home.
- Have you ever been loading your dishwasher and touched the door at the same time as your metallic sink basin? Zap. You forgot that the sink is connected to your water pipes, which are grounded.
- Have you ever touched the dishwasher at the same time as you were opening a cabinet? Zap. You forgot that the cabinet handles are metallic, and that they're screwed into brackets which run along the side of the cabinet doors, and that there's an electrical conduit box mounted on one of those rails on the other side of the kitchen.
So on and so forth. The point is that if your resistance to ground is extremely high, then you won't receive a shock by touching your electrified dishwasher ... but there are a near-infinity of ways that an electrical ground may be far nearer than you think, either by accident or design.
If your dishwasher were grounded properly, then the instant your fault developed it would draw enough current to trip your circuit breaker. Annoyed, you'd go to the breaker and reset the switch and it would instantly trip again. You would then call an electrician or a contractor who would immediately know that something is shorted to ground, and who would fix or replace your appliance. Inconvenience seems a fair trade, considering the alternative.
$^\ddagger$This is a toy example because I have no knowledge of plumbing or electrical codes and standard practices. I'm inventing a scenario which may or may not be realistic from the perspective of an industry professional, but I am a mere physicist so I am treating home wiring as a spherical cow in a vacuum.
