Neither seems insurmountable, but if you want to try and remove as many obstacles as possible in the search of those two things then the headphone jack is apparently one of the simpler ones.
Speakers, camera lens, physical buttons, charging, and data transfer are the remaining ones I can think of, and many of those have already been replaced in some models.
I think the headphone jack is a very practical component of the phone, and miss it regularly, but removing it does remove a few limitations on the designer.
At some point, in perhaps the not too distant future, I wouldn't be surprised if phones had been reduced down to look like not much more than a piece of glass. Maybe even a piece of flexible glass!
That's definitely been the trend for a while now, and things like edge to edge screens and wireless charging move us further in that direction. Thankfully neither of those seem to have necessitated the removal of some other function. There have been other casualties other on this path to simplification, such as the removal of the physical home button, but I don't think any which leave as big a gap as the headphone jack.
I’m typing this out on my iPhone 6 (which I will keep until it disintegrates because of its headphone jack) and it is plenty thin. I think only Apple themselves are obsessed with thin devices.