I push film because 3200 film isn't available in sheet sizes. Also, how about those low-light situations when f/2.8 gives you a 1/2 second shutter time at 3200? That's wide open for my 645.
When shooting in low light, things are going to be different from normal daylight. You have reciprocity correction, you have pushing the film, you have metering difficulties, etc. Things change.
Of course pushing doesn't mean a real speed increase. However, it is the difference between not having a workable photograph at all. Take a look at Occupy Everett photos in the gallery. That was done at f/2.8, 1/2sec. There is a *lot* of movement that can happen in 1/2 second, which means that someone's limbs can completely disappear. When people's heads are bobbing around, 1/2 second is too slow for the shutter speed. So I had to wait until they paused for a bit to have recognizable people in the shot.
As for TMax 400, it's OK to 1600, but at 3200 the lowest it will register on a gray scale is about the normal midpoint, and there's nothing beyond that. What I always recommend is that a person needs to do their own testing, and do it with an actual gray scale, like the Kodak test targets.