Why don't we see diverging nozzles or diffusers?
The basic answer is that pressure differential at the exit isn't what you want for thrust.  You want the exhaust stream to have velocity.  If it exits the nozzle with excess pressure, that extra pressure essentially gets converted into plume size (see the underexpanded streams on rocket first stages at high altitudes as an example).

This is why subsonic nozzles converge, and supersonic nozzles converge to a Mach 1 throat and then diverge.