Last year we laid a real slate floor in our kitchen. I believe that they are difficult to lay, not just the cuttingof them, but because invariably each tile is a different thickness, so to get them level is tricky.
Have said that, I love it. Yes it is cold and I'm sure no crockery would withstand being dropped on it. We needed to seal it a few times to stop it from absorbing stains etc and it needs to be resealed every year.
It never really looks dirty, but I'm sure a light stone would, in the same way any other type of light coloured flooring would.