Efficient players can get very favorable casualty trades without any air support whatsoever against the AI. Manual micromanagement (possibly with constantly updated spearhead orders) will trash anything the battleplanner can do for you, and it's not close.
A few examples as ridiculous nations:
Here's an example of invading a foothold:
Pin provinces so they can't contest, and overrun the port so you have supply. If the air is red, use AA.
I used it at the end of the battlecry achievement back when it still basically forced world conquest. Nuke infrastructure + ports to ruin supply and then surround 100's of divisions with low-consumption divisions of your own while they can't fight back due to org issues. It's a last-resort measure since setting it up takes so long, but it does help you wade through situations like "Japan has 500 divisions on home isles" or "UK has retreated 80% of its forces to its island" and you need to deal with them.
It's all a bit contrived for SP though. This game's base mechanics are broken in numerous ways, to the point of frustration/run ending nonsense. And though the game can screw you over with nonsense, once you know how it (doesn't) work you can trivialize it, too: