One good answer with proof and you can change my mind from being a skeptic to a believer.
Mars has regular dust storms. sometimes for months at a time and over most of the planet. We simply don't get any information during the dust storms, so most folks don't notice Mars then.
If you recall the Spirit and Opportunity rovers, both were disabled by dust storms. So Martian dust storms do have an effect.
Mercury doesn't' have any atmosphere, so no storms. It's the same with the Moon.
Venus has storms high up, but the atmosphere is so thick at the surface that it's like molasses and we really don't understand it's dynamics at ground level.
Jupiter has an atmosphere, though it's moons don't. The Great Red Spot is a hurricane that has been raging on Jupiter now for over four hundred years. We have no idea how long its been going on. There are dozens of other storms there at any time.
Saturn has a weird polar storm that is hexagonal. It also has moons with atmosphere, Titan is the most interesting moon in the Solar System for some scientists. We don't understand Titan's weather yet.
Uranus and Neptune are Ice Giants. They have atmospheres but also have surfaces. Not much is really known there. No more than a few hours of satellite observing time at each.
Pluto has an atmosphere and some weather. But we really only have a few hours of observation time for that 'minor' planet.
The sun also has storms across it's 'surface'.
So no, the Earth isn't unique in having weather. It is however unique in that we see it so much. That's because this is where we live.
You never see any storms on the SpaceX feed because they don't launch in bad weather. It has to be mild at the Cape and out at sea where their boosters land or they don't go. They've canceled several launches due to weather. So storms do happen, but they don't fly in bad weather, SpaceX just waits for good weather, which is why you only see good weather in the SpaceX video feeds.
You see the same sorts of selection in balloon flying. Hot air balloons don't launch during storms. Nor does SpaceX.
I don't understand just what it is that you don't understand here. Could you elaborate?