It seems to me that digging deep works, otherwise the war wouldn't be so slow, and the right way to conduct war for a force with air superiority is to use air mobility to take and hold. (especially for large, mountainous, not densely populated nation)
Unlike previous eras it is not viable for the opposition to try to counter attack with heavy armor and likes. Its a mutual siege situation, and air mobility and resupply a big force multiplier.
Still means a lot more casualties than rolling over the opponent's inferior armor like the Iraq war, but the whole tactical situation was a mistake by the Iraqis to begin with, from a hindsight perspective.