It’s interesting that the OP seems to favor a unified service. (I seem to get that impression for the post, even if not implicitly stated.) Historically, as weapon systems became more numerous and specialised, the services (with their command and planning staffs) seperated to concentrate on their specialties. This didn’t happen because of “tradition”, it happened despite tradition.
In the years leading up to the Napoleonic age, the major powers did indeed have what amounts to a unified service (a Field Marshall in overall command of the forces present, with the Admirals under his command taking care of the technical details), with GB being a notable exception.
However, as the industrial age came around, and the technical knowledge required to best use the weapon systems available required specialisation, and eventually seperation, of the armed services. An Army General has already too much to learn about war fighting with ground troops (besides the nebulous “inspirational leadership” skills all leaders need to coax their troops to put themselves in grave danger, you also have the skills of logistics and supply, force concentration, communication and control, battlefield manuever from the squad level all the way up to Corps level, etc.) to expect that they also have to learn about the navy side of things (the “fleet in being” concept, navigation, ship maintenance and repair, convoy routing and intercept, distant blockades, mine warfare, and so on).
Real world example: In the 20’s, the Royal Navy aviation units were placed under the care and feeding of the Royal Air Force.
Since budgets were (and still are not) infinite, priority for those defense funds went to bomber development. The designs (and aquisition) of carrier based aircraft suffered. (Carrier aircraft have a while slew of required features that shore based aircraft do not.) Great Britain went to war in '39 with carrier aircraft that were obsolete at the very start (even though the RN had regained control of it’s ship based aircraft in the mid 30’s).
It’s difficult to say exactly what effect this had on the war. It shouldn’t be a stretch to assume that if GB’s carrier based force had better aircraft (and the design bureaus set up and humming, producing newer designs), the carrier force would have had a more positive effect on the war (from GB’s point of view). Can you imagine the “Hunt for the Bismark” if the Victorious, Ark Royal, et al, had the combat capabilities of the USN Dauntless dive bomber types?
Note: The USN was marginally better in May '40. Dauntless SBD’s, Devastator TBD’s, Buffalo Fighters, compared to the RN’s Gloster Gladiator’s, Blackburn Skua, and Fairey Swordfish.
The IJN had, arguably, the most capable/advanced aircraft, the A6M “Zero”, B5N “Kate” torpedo bomber, and the D3A “Val” divebomber.
End Note.
The US Army was in control of the Air Force through WW2, and did a fairly decent job of it. Arguably, the bomber design (B-17) received more attention than the fighter designs in the late thirties, but the US industrial base was flexible enough to get out better fighters (P-40 vice P-36, F4F vice F2F) just in the nick of time…