Why would Earth have stable weather patterns if it stopped spinning and vigorous weather if it had a much faster rotation?
Weather modeling is crazy complicated so I don't want to make this sound absolute, but Venus virtually doesn't rotate and it has much faster trade winds than Earth.   Venus has low surface wind speed but that has to do with the consistent temperature all around it's surface and a very dense almost viscus atmosphere.

You might not get hurricanes with a slow rotation and virtually no Coreolis, but you'd still get weather.  The heavy cold air from the night side of the planet would sink and the hot day side of the planet would rise, and you'd get a constant re-balancing of density and a steady wind and likely a lot of rain as the air cooled on the night side, perhaps continuous rain at a certain time during the night (the same process that creates dew but much bigger).

Some good answers on a related question here.