Why not?
Checkerboard floors can be done in smaller scale tiles if you'd like, and were quite common in the 40's and 50's when houses were smaller.

This place has the 9" pattern squares which helps so you don't lose the pattern.
black and white continuous vinyl checkered floor

www.checkeredfloor.com

They have it in small width size and large width size for small or large projects. Like kitchens & garages for the large size width and bathroom, laundry or car trailers for the small width. Only takes about a week to get.

Check out daltile.com It's their unpolished porcelain. Look at their Match Point series(jet black and Pure White), Formula series (Union Black and Theorem Ivory) and Plaza Nova series (Black Shadow and White Image). First 2 come in 24x24 and the 3rd option is 12x12 tile.