It's a genre thing. There is a whole class of these grid-based dungeon crawling games out there and even in the recent ones they stay true to the restriction.
BTW - this vid seems to show Legend of Grimrock playing with mouse-look: https://youtu.be/xALsxZv0pwg?t=8m53s
BTW 2 - just discovered that cursor keys can rotate. WASD for motion and L/R cursor keys to rotate is waaay better for me.