I find log cabins made with 1 or 1.5 inch strips to be so much more graceful and visually pleasing than the wider strips. True, they do take a lot more time, and they can become quite heavy-- there's a lot of fabric in the seams. But the fabrics blend much better fora graphic look.
I've made some log cabins quilts where the strips were not cut uniform widths. They were all between 1 and 2.5 inches, but no exact measure. I then trimmed the finished blocks to be a uniform size, and there was surprisingly little discrepancy in the vast majority of the blocks. The finished quilt is one of my most complimented projects, and most people don't even see that the strips are not uniform widths-- they just comment on how it makes a really cool pattern that almost glows. After that success, I doubt I'll ever fuss over exact cutting and piecing in a log cabin again.
RST