J.B.
We had slate in the kitchen and dining of a previous house. Slate by nature isn't a smooth tile. There are ridges that little toes trip up on. It does continue to deteriorate after being installed, meaning pieces or slivers of it will flake off. It is a delicate choice for tile. It can be difficult to install due to the uneven surface on both sides.
There may be finished options (where one side is smooth?!?!)
I wouldn't choose it again.