Are there countries that don’t have both Armies and Navies? Presumably not having a Navy is pretty common in landlocked countries. But what about, say, being so wet focused that all infantry (and any other relevant army bits) are used as marines and subordinate to the Navy?
USA-wise, I think two useful lines of argument would be r&d and chain of command.
Weapons change. Is it illegal for the Army to upgrade? Surely semi-automatic rifles are ok to replace muskets? What about machine guns? Hmm, how about improving range and size of your artillery? Instead of horse cavalry, can we do something with internal combustion engines? Hey, with this flying wing we get much better reconnaissance, and less cases of scout being shot. On the Navy side, you go from cannon, to really big cannon, to torpedoes and guided missiles, to putting helicopters on ships for use as anti-submarine weapons.
The constitution does not specify weapons and equipment to be used by the army and navy. If the army wants boats because they’ll be needed in the next war, it’s not illegal for the Army to have a naval arm. Arguments over jurisdiction, sure, but we already have Army vs Marines. And if Army or Navy thinks planes or long range missiles will win wars and reduce us casualties, then you need a better anti argument than “well, the Constitution didn’t say they can, therefore they can’t “
On the other hand, something that isn’t in the Constitution but was talked about a lot, is civilian control of the military. Rules about declaring war, with or without Congress, quartering of troops, paying for it all, lots of rules to keep the military under control. Okay, so we have a civiliand Commander in Chief. What does the Constitution say about below that level? A big blob of come as you are army might work, but kind of hard to control and oversee. Why not divide it up somehow so the CiC can be more efficient, and can be sure they know what anti-civilian-control is going on in the military.
So, let’s split our military up into Tweedly-Boppers, Rondos, and Fhtagn. (Or, take Army, Navy, Marine, etc and translate to your preferred non-English language) What goes in each group? By your logic, nothing. If the only tags you’re allowed are Army and Navy, that really limits how to efficiently divvy up your forces. Hmm, that also means that armored cavalry have to be on horseback, and having commanders by region is illegal too. After all, who ever had an army and divided it by grouping all units in a certain region? Oh, we also need to disband the Marines, coast guard, noaa, and uniformed medical, none of those are named army or navy.
Back to the Tweedly-Boppers. Over time, some units have really changed roles and can’t be efficiently run the same as normal units. Why not split them? The Tweedly-Boppers keep the role of combat on plains and in forest, and the new group NarfNek is all mountain warfare. Does the Constitution make it illegal to have better organizing and better civilian control?
So, if the claim is Air Force is unconstitutional because of name and role. That fails because making air a separate service is (supposed to) more efficient, and allows better/easier control by the President. Requiring the use of one of two words (army, navy) means you cant make military more descriptive of what they do.
If the claim is uncon due to “fighting in air”, that fails because the military should be allowed to decide what equipment it needs to win wars. Giving a grunt a jetpack doesn’t suddenly make them verboten. When there are no explicit rules given, saying “no aerial combat stuff” makes as much sense as “no gunpowder based weapons”, both make you fail at the ‘common defense’ thing
And a couple things from checking the text. The US is not limited to Army and Navy, Article 5, the Militia is separate from the land and naval forces. Also Article 1 section 8.
“Forts, Magazines […] and other needful Buildings”. So there’s your Air Force infrastructure handled.
Art 4 section 4 - the US has to protect states from invasion. For that to work, it has to have the power to have forces for whatever form of combat. Kinda silly to say “okay, yall are protected as long as nobody sends a plane or a cruise missile”