Nobody really answered your question so I will. Copious amounts of press fit headsets still around on new bikes...more off road and generally metal bikes...steel, Ti and even Al. Threadless went away principally because loading of headset bearings is foremost axial aka compression. As a result angle seated bearings are used which can sustain higher thrust loads. Under compression as with integrated headsets, when most of the load due to rider weight is vertical (cosine of Head Tube Angle) there is no reason for threads as the entire headset is under compression due to the weight of the rider. Coincidentally press fit and integrated headsets became more prevalent when threadless steerers became prevalent.

So answer is...load is axial and weight of frame plus rider + top of steerer screw keeps upper and lower bearing in compression and threads are unnecessary.

A real philosophical argument and honesty a companion question is...why did BB's move away from threaded to press fit. This is a deeper engineering discussion and most know that press fit headsets are generally more reliable than press fit BB's. This is again due to loading. In the case of a press fit BB, principle load is 90 degrees to direction of press fit. This is why BB's in spite of preload are so problematic. More than you asked for but related.