Apple already has the SE for the low cost market. They have positioned the mini as the mid-range. What they're missing is a high-end small phone. I'd happily pay for it.

The current SE isn't a small phone; it's a previous-era-of-design phone. It's a phone from before phones gave you as much screen as would fit on the front face of the body. If you want that, you can just buy any new-old-stock phone from 5 years ago; they're all cheap, they're all that size, and they're all (IMHO) painful to read or watch anything on.

A low-cost small phone would be the opposite of the SE: not good-specs, bad-screen; but rather all-screen, bad-specs. An iPhone Mini minus-minus.

Agreed, I think this is not only for the reason of cheap manufacturing (I doubt it's a lot cheaper than just reusing the iPhone XR case). I think it's just a conscious disincentivisation (word?) from Apple to avoid cannibalising their mainline models :) I'm surprised it's so popular, because I really don't miss the bezel. All-screen phones are a great advancement.

If I had an iPhone I would seriously miss the fingerprint scanner but this is not an issue on Android, the in-screen option works amazingly well.

iPhone 13 mini.

Having said that, the specs of the SE are nothing to sneeze at.

It doesn't have the full camera.

Edit: I'm not sure what the disagreement is but it's objectively verifiable that the 13 Mini does not have the same camera setup as the 13 Pro.