Space is not a constrain in many flagship phones. Check this comparison of (unofficial specs) s24 vs s8 (0.5mm appart. S8 also had sd card slot)

https://m.gsmarena.com/compare.php3?idPhone1=12773&idPhone2=...

This is the datasheet of a generic 3.5mm It is thinner than that: 3.2mm.

https://www.cuidevices.com/product/resource/sp-3530.pdf

Just the tip is 3.2 mm. Ring and sleeve are 3.5 mm.

But phones aren't really that thin, especially with the camera lenses. Why didn't they just put the 3.5 mm jack on the other side from the cameras, protruding a little bit from the rear housing, exactly enough for the phone to rest stably on a flat surface without rocking?

That was the stated reason. The iPhone 14 is 7.8mm deep without a 3.5mm jack the iPod Touch (4th gen) was 7.1mm with a 3.5mm jack.

Additionally as other have stated there are thinner (2.5mm) audio jacks.

The iPhone 14 has a glass case while the iPod Touch 4th gen had a metal case. That alone accounts for a significant difference in thickness of the internals of the device.