Grass, as in lawns are a little bit different than wild fields. Most people design good drainage into their lawns so water doesn't pool and flows off quickly. Drainage is key to permeability, the longer water stays on soil, the more time it has to absorb into the soil. If it flows of quickly it will never reach full saturation.
After it permeates, then what? The water still has to go somewhere, and usually it's into nearby ditches (and then streams, and then rivers). As well, with any larger rainfall the local water table below the grass will fill up quickly- now the water is running on the surface.
Permeation is definitely good, but having more stops before it gets there is important to prevent floods.
(To be clear, I'm not expert on this at all. But I did marry one, and you sort of absorb a lot just from conversations over dinner).
