I feel like having it any distance above the ground leaves a gap that dust and junk finds its way into and also stuff gets lost under

Have to, probably not. But they are functional

Depending on how the couch is built, not having feet can scratch your floors. I had one that was like, a bunch of springs, and it really sagged and moved with you

You probably get better airflow too. If you live in a humid climate that can be important so that moisture doesn't get trapped inside and leave you with a moldy couch. But also like, sweat and stuff

It may not be as comfortable at the lower height without the feet, but if you have short legs, you wouldn't have to worry about that

So, no, you don't "have" to.

A bunch of couches have staples or nails on the bottom rim which will scratch up or tear your carpeting, or damage the lower couch material by rubbing against the ground. Even if you're not moving the couch, sitting and getting up will still create movement enough.

If you don't like the couch feet that came with it, you could always attach shorter or stubbier feet so it both won't hurt your flooring and you could create a very narrow gap that wouldn't have the problems you described.

I went the opposite way, I put bed risers under mine. Wife didn't like it because she's short, needed help getting up on it, but I loved it. Ultimately they came out.

If I owned the place, I'd build a mount for the sofa. Steps leading up to the front but it would be well raised in the back and I'd put drawers under it. Not a DIY guy at all, so I'm not sure how feasible that would be. Drawers could contain linens for guests, extra pillows, stuff like that.