Don't get over-centred on uniform colour. Military money all comes from one pot and Ministers do not spend more on 3 separate (land+sea+air) Forces than they would on 1 or 2 multi-mode Forces. Smuts 1917 recommended splitting out Air (and integrating till-then overlapping Land-Air and Marine-Air), in part because Ministers feared civilian panic from Zeppelins, and in part because UK's own Paralysers were drifting, not well-managed in the grotesquely overloaded Ministry of Munitions competing for materials with the Air Members of the Board of Admiralty. Right mess. Accountability; not me guv! one fall-guy needed; ambitious personalities (Lloyd George, Churchill). "Independent" did not mean "extra money": it meant targetting separately from support of monitor- and artillery-bombardment.
Imperial Japan and USArmy/USNavy (till 1947) found it entirely suitable to run Air Arms integrated within discrete land and naval Forces. USN continues to integrate Air within its Force, even while segregating its Navy and Marine Air. Neither Belgium nor Canada have lost capability by re-naming Air as Component within unified Armed Forces. Unit esprit de corps is not dependent on reporting chains of Top Brass bidding for budget. There is no objective "best practice".