If you push Portra400 after underexposing it a stop, you'll get a little more grain (not the best for skin), you'll change its tone a bit, and you'll increase contrast too...
400 is very fast: with a fast lens we can use it in most situations...
If 400 pushed to 800 was great, Kodak wouldn't make Portra800.
I'm familiar with Push1 and Push2 in a Q certified lab... For a certain look, and only if the scene was a low contrast one, I would underexpose 400 a stop to push it to 800 with development, but not in every situation or as a common possibility. I would never push Portra400 to 1600.
I wouldn't push 800 to 1600 either. A digital capture makes more sense in color when light is poor for film.