The problem is that when you push an object, the push happens at the speed of sound in that object. It's very fast but not anywhere near the speed of light. If you tapped one end of the stick, you would hear it on the moon after the wave had traveled the distance.
For example, the speed of sound in wood is around 3,300 m/s so 384,400/3,300 ~= 32.36 hours to see the pole move on the moon after you tap it on earth.
There are multiple forces at work in a converging rocket nozzle:
The exhaust is pushed outward faster since the hole is smaller, giving the rocket extra thrust
The exhaust hits the wall of the nozzle as it gets thinner, braking the rocket
These two effectively cancel out, which is why the actual effect of making the nozzle thinner/converge is that it increases the back pressure within the engine (constricted space, smaller hole), essentially (idk how) increasing the efficiency of the fuel burning.
However, when the nozzle gets too thin, the exhaust becomes faster than its speed of sound. Since the pressure travels at the speed of sound, it can now not actually get back into the engine anymore. So that's the limit of how thin you can make the nozzle. The pressure has to get back into the engine to have its effect, so you can't make the exhaust travel faster than its speed of sound.
If any of this sounds wrong to anyone, let me know, I'm not an expert in this.