I'd add a few things to Sounds's very good response.
Firstly, lifting a vehicle improves the angle of approach. If you're approaching an obstacle or even just a steep hill, if the vehicle is too low to the ground, the front bumper will hit it before the front tires do and so you won't be able to go any further. The effect is usually even worse if you're trying to back over something.
The other thing is suspension travel. Lifting the vehicle allows the wheels to move further up and down, which means you can move over uneven terrain without the tires rubbing on the wheel wells.
One other possibility with the lifted vehicles you're seeing with normal tires is that the owner has a separate set of wheels for off-roading. High performance off-road tires are expensive, wear quickly and perform poorly on-road and so often owners will keep a separate set of wheels for just tooling around town (or driving hundreds of miles to get to Moab or wherever they like to off-road), and won't throw on the expensive mudders until they're actually ready to use them.
But I will agree that SPS is probably the largest factor involved in lifted vehicles you see in Seattle.