Usually, mitered square projects are done on relatively small needles. They are perfect for showing off multicolored yarns (especially hand-dyed yarns or sock yarns), because there is never an opportunity for the colors to pool in unattractive ways. While incredibly simple to knit, the geometric lines of mitered squares appeal to people who like M.C. Escher designs, too. I've always liked the effect, but like I said, couldn't find the right project.
Well, when I found the right project, it wasn't with sock yarn or a luscious hand-dye. I used a super chunky acrylic blend and size 13 circulars. The result was a fun variation on your basic patchwork throw. It has more visual interest than simply assembling squares knit in various colors and was more enjoyable to knit, without being complicated. Since I didn't always pick up the stitches for the next square on the same side of the blanket, it came out reversible. There was no sewing to do at the end (always a perk in my book). I also played around a little with the directionality of the squares, which is another fun option with mitering.
Scaling up my mitered squares to a super chunky yarn really emphasized the texture of the garter ridges and made for a delightfully squishy texture. It doesn't have any of the clean, modern, precise look of small mitered squares. Instead, it has a casual, rustic look that reminds me of certain quilt patterns. I would definitely recommend this, or some other project made of large squares (rug, pillow, etc.) as a fun introduction to the world of mitering.
If you're interested in learning to make mitered squares, the following video (from Knitting with Cheryl Brunette on YouTube) is a good tutorial. The blanket I made used super chunky yarn, size 13 needles, and started with 61 stitches on the cast-on edge (30 stitches on either side of the central decrease).