Personally I see no problem whatsoever in somebody doing this for commercial gain. Pilot Officer Penketh's body was recovered from the site at the time and was returned to his parents in Hove. He was cremated at Brighton (Woodvale) crematorium (from the CWG website).
The site is thus not a war grave. I suppose it could be argued that the remains of the aircraft (such as they are) are still government property, but if someone is going to the trouble to dig them up, I'd say they are theirs to dispose of as they see fit. I cant see the RAF museum, for example, wanting to take charge of a pile of scrap metal, unless there is something special about this particular Spitfire.