It's always possible on a high resolution, small sensor camera that the lens isn't up to resolving everything the sensor is capable of capturing.
Still, though, I'd doubt that 4mp of resolution is all the lens is capable of.
If you're viewing at full screen, you won't see any difference. If you start zooming, it will be there-I all but guarantee it. It may not be 20mp but if you really see no difference between 4mp and higher on magnification, it's likely either poor technique or a serious issue with the camera.
And if the answer is that you'll never view at more than full-screen res(say 1920x1200-I know little of the 15" MBA but if it's like the older 15" retina screens the default scaling is even lower at 1440x900) or print larger than 8x10, there's still a big reason to shoot at higher resolution. That reason is cropping. I can't begin to tell you, too, how nice that is to have on high resolution cameras.
BTW, my most used camera these days is my 20mp Nikon D5. I use it in favor of the 45mp D850 because I like its straight out of the camera color rendition and appreciate its high ISO capabilities. I'm satisfied with 20mp. I'm fine even with the 16mp from my D4, which I use as a second camera along side the D5 due to handling similarities and also similar outputs, or the Df, which is the same sensor as the D4 but packaged in a very different(in a way almost special purpose) body. I'd not intentionally handicap myself going down to 4mp, though...
As a few other thoughts-first of all I'm not a fan of throwing away data, and that's what shooting at lower resolution than a camera is capable of is doing. I also am a big advocate of RAW-I use to do RAW+JPEG but now don't even bother with that(I'd rather save the buffer space).
Second, storage is cheap these days. My go-tos are 64gb CF cards in my CF cameras and 128gb CFe cards in my cameras that use those. Cards are not meant for long term storage, and I am always concerned that just leaving a card "parked" in a camera and saving every photo you've ever taken on it is a recipe for disaster. Any "interaction" of a card with another device(even plugging the camera into a computer to download files) introduces another path for data corruption. This can not just impact old files on a card but your ability to access recent ones or even write new ones.
I'm particular about card management-after I pull photos off a card I hold on to it until I copy it onto external storage, and then format it in a camera before cycling into one of my card wallets. Even then, I always format a card when I first put it in a camera.
A few years back, I was at a family even where I'd fallen into being official photographer, as happens to me sometimes. I was using my Nikon D800, or maybe I had my D810 then-I don't know but it was one of those. In any case I am a few minutes in and all of a suddent my camera quits writing to the card. In the immediate I grabbed my backup(I think I had my D600 then) and kept right on, then a few minutes later changed cards in teh D800 and continued on, or maybe just pulled the CF and used only the SD in it. Whatever the case, fortunately the card was recoverable but I didn't trust it after that. Sandisk did replace it under warranty, fortunately, especially as 64gb CF cards never have been cheap.
