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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.

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.