Noticed this while looking at several MH-60R/S paints, and many of the newer Bug/Super Bug schemes, loads of color. As if it's a competition between squadrons. Is the Navy using this as some form of advertising?
Been a tradition for decades that was somewhat suppressed after advent of subdued TPS paint schemes. Having an "airshow" or CAG aircraft is good for morale (and patch sales so, yes, it is a form of advertising) and squadrons always compete for looking good.
Japanese are always great customers for squadron patch and other memorabilia hence dramatic paint schemes of many CAG-5 aircraft that are arguably the most colorful in the Navy

070412-N-8591H-066 MOUNT FUJI, Japan (April 12, 2007) - Aircraft assigned to Carrier Air Wing (CVW) 5 perform a formation flight in front of Mount Fuji. CVW-5 is embarked aboard USS Kitty Hawk (CV 63). Kitty Hawk operates from Fleet Activities Yokosuka, Japan. U.S. Navy photo by Mass Communication Specialist 3rd Class Jarod Hodge (RELEASED)
CVW-5 Hornet squadrons compete for most colorful for their Japanese fan clubs and the rest of the Navy Hornets as well

080401-N-6106R-008 PACIFIC OCEAN (April 1, 2008) F/A-18 Hornet strike fighter aircraft assigned to Carrier Air Wing (CVW) 5 fly above the aircraft carrier USS Kitty Hawk (CV 63). Kitty Hawk and the embarked CVW-5 squadrons deployed in early March and will undergo several training evolutions over the next month. U.S. Navy photo by Mass Communication Specialist Seaman Stephen W. Rowe (Released)
"Chippy Ho" in 2006

060621-N-3136P-039 Philippine Sea (June 21, 2006) ? An F/A-18C Hornet assigned to the ?Dambusters? of Strike Squadron One Nine Five (VFA-195) conducts a fly-by during flight operations aboard the conventionally-powered aircraft carrier USS Kitty Hawk (CV 63) during Exercise Valiant Shield 2006. Valiant Shield focuses on integrated joint training among U.S. military forces, enabling real-world proficiency in sustaining joint forces and in detecting, locating, tracking and engaging units at sea, in the air, on land and cyberspace in response to a range of mission areas. U.S. Navy photo by Photographer?s Mate Airman Jimmy C. Pan (RELEASED)

080828-N-9565D-099 PACIFIC OCEAN (Aug. 28, 2008) An F/A-18C Hornet assigned to the "Dambusters" of Strike Fighter Squadron (VFA) 195 lands aboard the flight deck of the aircraft carrier USS George Washington (CVN 73). George Washington is transiting off the coast of Southern California conducting combat operations efficiency evaluation with Carrier Air Wing (CVW) 5. George Washington is en route to Yokosuka, Japan, where the ship will replace the aircraft carrier USS Kitty Hawk (CV 63) as the Navy's only forward deployed aircraft carrier. (U.S. Navy photo by Mass Communications Specialist Second Class Clifford L. H. Davis/Released)
Diamondbacks also pumped up the volume on their markings after arriving in Japan (their local fan club responded with creation of the J-Backs who buy anything coffee mess produces)

070907-N-8591H-122 BAY OF BENGAL (Sept. 7, 2007) - An F/A-18F Super Hornet assigned to the Diamondbacks of Strike Fighter Squadron (VFA) 102 makes a final pass before landing aboard USS Kitty Hawk (CV 63) during exercise Malabar 07-2. This multinational exercise includes naval forces from India, Australia, Japan, Singapore and the United States. Kitty Hawk and embarked Carrier Air Wing (CVW) 5 are currently conducting their summer deployment. U.S. Navy photo by Mass Communication Specialist 2nd Class Jarod Hodge (RELEASED)