I use one regularly. You can get a better 'saturation' in woodland situations. No you don't need a blue blue sky but cloud definition can help. It is light and simple to use - not overly expensive and doesn't take up much room.....What's not to like! Put it on when necessary or leave it OFF. Not every shot needs it. Having the choice is a wonderful thing!
I always have a polarizer with me for landscape photography. You have to watch out for uneven polarization across the sky when using a wide angle lens.
How often do you landscape photographers use a circular polarizer?
I would have to guess for me it would be 60% / 70% of the time. That is because I will continue shooting between the morning / evening golden hours. The polarizer cuts lots of different types of reflections and helps with color saturation. I will also use the polarizer to give some pop to rainbows.