Marine squadrons routinely fly off CVNs with their F/A-18 Hornets. Institutionally, they have a long memory of not having carrier support in WW2, so they cling to this notion of operating their own air force.
For more details on exactly why the USMC is so afraid of being without carrier support, see accounts of the Battle of Guadalcanal. I recommend "Helmet For My Pillow" by Robert Leckie, which was also one of the books used as a basis for the HBO miniseries "The Pacific".