Non-round eyeballs?

Somehow I always find hard to model characters out of concepts with impossibly huge eyes, when I go to modeling, I can’t quite fit the eye inside the skull.

my question is, why so few people “cheat” and make a non-spherical eyeball, is that because rigging becomes slightly harder or is there some deeper underlying reason?

eye moving on its orbit is a problem. normally a cartoon “saucer/spoon”-y eye has the iris as a plane sliding on top of it instead of the full eyeball moving.

rigging these correctly so they don’t look at the wrong focus point or break the suspension of disbelief requires technique

I thought in using a lattice to squish the eyeball inside the head but I guess I’ll try this separated iris thingy, maybe with some normal transfer it can look seamless.

That’s exactly what I did. I use a lattice to distort a sphere for the eyes of my character. Works perfectly.

don’t the oval eyeballs pop out when he’s looking up?

No. It’s just a sphere that rotates inside the lattice. You just need to make sure the sphere has enough subdivisions so it doesn’t wobble as the eye rotates.