While obviously I've expressed my desire to totally overhaul the supply system, you are probably right that it wouldn't be necessary to make good progress towards making late game combat more enjoyable.
For me, I think a comprehensive yet still relatively simple (i.e. only changes numbers) solution to late-game combat would involve a three pronged approach of 1) changing how units scale, 2) changing how units interact with and compare with one another, and 3) reducing supply caps, with the goal of keeping total army strength the same, just spread over fewer units that are more distinguishable from one another. This should ideally help with both balance and player experience.
1. By changing how units scale, really I just mean making them scale harder. Currently, as a relatively stereotypical example, the melee infantry line, in terms of CS, scales a total of 1000% between its first tier and final tier, averaging a 43% increase in CS per upgrade. However, the first four upgrades average +48% per upgrade while the final three average just 28%. Obviously the later-game units also gain some promos and other extra attributes, but it still stands that generally speaking the later in the game the unit upgrade, the less impactful it is on gameplay. There are a few notable exceptions to this, such as the siege unit line, but in general this holds true. Even just minor increases to upgrades compound over time to have much stronger units. Like if the final three upgrades averaged +35% instead of +28%, mechanized infantry would have 94 CS instead of 80, an 18% increase, meaning 5 units have nearly the same total CS as 6 do now. And if you did +40%, then mechanized infantry would have 105 CS, a 31% increase, thus making 3 units have nearly the same total CS as 4 do now. However, it isn't quite this simple as how units with different CS values interact doesn't change linearly with changes to CS values, but I think that's largely immaterial to the point I'm trying to make. Proportionate increases to production cost and gold maintenance would necessarily have to follow as well.
2. As a lot of people have said, the Tank line is just kind of busted. Sure, doing stuff like making them cost 2 supply slots or use 2 copies of oil might address that, but it would only do so indirectly and superficially. The fundamental problem with Tanks is that they are just wholesale stronger versions of Infantry. Though not perfect, I think that the distinction between ranged units and siege units is a good model. Field Guns gain Indirect Fire while Gatling Guns gain Covering Fire, sharply pushing the two branches into different directions. And then Artillery gets range but a smaller increase to RCS and Bazookas get Anti-Tank Rounds, further differentiating the two branches. On the other hand, the only meaningful difference between Armor units and Infantry units, beyond the former simply being stronger, is that Armor units are faster (even though railroads often diminish the importance of this bonus). Once both types of units are in the same position, they operate the exact same way, but Armor units just happen to have way more CS. My thinking is to overhaul/remove the Armor Plating promotion, and instead of having Tanks get a bonus defending, have them get a bonus to attacking. After all, Armor Plating does essentially the exact same thing as Entrenchment/DFPs, even though Armor units are ostensibly supposed to be your shock units that bust through enemy lines and create holes your infantry fill in. Possible replacement Armor promotions could be one that gives ranged attack before their melee attack (like the Impi), one that gives area damage on kills or ending your turn next to the unit, or even just a simple +x% CS modifier while attacking like Commandos.
3. This is the most simple one. If you increase the strength and cost of the final tier of units by say 33%, then to help keep everything else in the game in balance you would also need to decrease supply. I also think this is an opportunity to kill two birds with one stone, in the sense that any changes we make to decrease late-game supply should disproportionately affect large empires, as currently I think large empires have way too big of a supply advantage. Thus, taking away flat supply from the Military Academy and decreasing the supply from population on the Military Base are probably good ways to reduce supply.
Also, re: air combat, I've just started using the air unit action shortcuts and that has dramatically improved my experience with air combat, though healing/upgrading is still pretty annoying and en masse attacks are definitely not strategically optimal all the time.