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Does it make sense to always leave the polarizing filter in the Filter Holder? 

We recommend leaving the polarizing filter on the lens only if it really has a use. For landscape photography or a tour of a city, the filter can usually stay on. 
Because in both situations, there are often mirroring and reflections that can be compensated for with a polarizing filter. It would make little sense to keep removing the filter from the camera. A polarizing filter usually does not have any major negative effects if you simply leave it in the filter holder. 
However, similar problems can occur as with a UV filter. The polarizing filter absorbs a little light and can have a negative effect on the images in certain situations when you don't actually need it.