That all depends on the operation.  I work on a milling crew (the group that uses a mill to tear up the old road and load the millings into trucks so that the new asphalt can be laid), and I'd say 98% of our jobs are mill and fill (mill up the old asphalt, clean the cut, fill with new asphalt).  Generally the only times we don't perform mill and fill is on a total removal (milling the old asphalt until we reach base rock/dirt), a parking lot for a new building that doesn't have the correct slope to properly drain water, or a subdivision that has curb recovery (milling out the previous layers of asphalt that have risen above the level of the concrete curb).  I think most of the time that the roads are left open like that are city or county projects, performed by the city or county themselves.