Can the crust be compared to an arch?
An arch is a poor analogy for tectonic plates.  The lithosphere is  supported beneath by the mantle, unlike an arch which is unsupported beneath.  If the lithospheric plates were only held together only by lateral stress, friction with surrounding plates and gravity, how would they move relative to each other?  How would forces at the plate interfaces vary?  How would subduction work without the whole thing falling apart?  I am not a geologist but I cannot see how this arrangement would work.  

The mantle "fluid" that sits underneath the lithosphere convects and drives plate motion.  It accepts subducting plates and emits new oceanic crust along the mid-oceanic ridges.  The support everywhere underneath the lithosphere by the asthenosphere makes an arch a poor representation for the physics at work.  

Yes, you are correct that at the tectonic plate edges there is lateral stress and friction and that the whole plate is subject to gravity.  What you are missing is  that the crust is everywhere supported underneath.  An arch relies on the lateral stress to stay standing while tectonic plates do not.