And not one of them is owned by California. Just sayin’.
Well hello stereographic projection. I see you’ve met my friends into photogrammetry and remote sensing.
I’ll just leave you alone.
I can personally attest to this, from my experience as a Kerbal Space Program astronaut 
Pretty much all those links are irrelevant to the question you asked.
Most detailed remote sensing systems look straight down at a fairly small spot on the ground.
If your satellite orbits at, say, 5 degrees orbital inclination then “straight down” will never be farther than 5 degrees above/below the equator. So you’ll get an excellent view of the tropical-most tropics and not see any of the rest of the Earth. But you will cover that small swath of ground over and over and over very quickly.
Conversely, if your satellite orbits at, say, 60 degrees orbital inclination then “straight down” will cover everything from northern Canada & much of Russia down to all the and in the southern hemisphere except Antarctica. You’ll cover any given spot less often as you sweep north and south while flying eastwards as the Earth slowly turns beneath you. But you’ll cover a lot more spots.
Here’s a simple map World Atlas / World Map / Atlas of the World Including Geography Facts and Flags - Worldatlas.com - WorldAtlas.com with 15 degree latitude lines. Compare the ground swath that covers the Earth from the equator out to +/- 4 latitude units versus one that covers from the equator out to +/- just 1/3rd of a latitude unit. Massive difference.
I’m not sure what ellipse you’re referring to, since the ground track will be a band bounded by a couple of circles, not an ellipse. But I think that what you’re missing is that the Earth is rotating underneath the satellite. An equatorial satellite will only ever see a band near the equator (with how wide that band is being determined by the satellite’s height), but will see that same band again and again, every orbit. A polar satellite, by contrast, will see a different strip of land on every orbit, and unless you carefully contrive to get a resonance between the orbital period and Earth’s rotation, will eventually pass over every point on the planet.
What LSLGuy said.
Google satellite ground track and you can see all kinds of funny images, most of which look a bit like a sine wave where the peaks don’t quite overlap.
This is a good thing, since, as said, you eventually cover every spot within that band of latitude. A purely equatorial orbit is boring in comparison and is just a straight line along the equator. That’s ok if your orbit is really high and you can see (close to) half the Earth at once, but not so good if your orbit is low and the horizon is not that far away.
There are some crazy orbits with figure-eights and other weird shapes; these typically have a highly elliptical orbit and a carefully-chosen orbital period. These have their uses, but wide ground coverage over the whole Earth isn’t one of them.
Thank you to all three of you.