Users invented the inverted method. I think it began with Scott Marquardt in Chicago. I resort to that rarely when I have some coffee that was ground too coarse. But I don't steep because that increases bitterness. I just stir and immediately twist on the cap and filter, revert and press.
If your grind is between espresso and drip, the normal method works great. The tiny amount of brew that drips before you press has no perceivable effect on flavor or richness. I use the normal method every day.