There are examples of large slate tiles being used in the 'first' Eichler Book: 'Eichler Homes. Design For Living'
Personally, I think tile is the most architecturally appropriate material for these homes. So, I say go for it!
But the use of dark slate is still a matter of hot debate. :)
Why is dark slate a subject of debate?
Dark slate (dark flooring in general) seems to be disliked by the purists for being out-of-place with "mid century modern" - - the dislike is purely esthetic and is not function related although dark floors seem to require more room lighting when the sun goes down. It does seem that most people prefer lighter color shades because anything that is brighter is generally preferred whether or not it is Eichler related.
In the Fall 2003 issue of Modernism magazine there is a feature devoted to a 1958 mid-century modern home with dark ebony flooring. The owners say it is original to the house. The floor looks like slate but is actually high-quality linoleum. It works well with the rest of the color scheme that they have in furniture, wall colors etc. The ceiling and beams are also a dark color--very dramatic.
we just installed about 900 square feet of Brazilian multi-color slate in our kitchen, entry and atrium. It looks wonderul! The job was done by a company I would highly recommend. You can e-mail me for their name: firstname.lastname@example.org
Two homes in our area have the dark grey slate and it looks beautiful. Do you know Loni Nagwani? She is an RE agent that lives in a Willow Glen Eichler on Fairwood. Her slate floors are gorgeous (20x20) and I am sure she would be happy to show them to you. She advertises on the RE section of this site.
Most of our house is tiled in African westcountry slate (on top of a new radiant system). We absolutely love it. We were definitely drawn to the more varied colored flavors. The one we chose has a rich and organic feel to it (think wood or cork).