Bias gives the quality of stretchyness. This is very useful if you are a wee bit short on fabric for your binding, such as if you make a slight mistake in measurements. The bias allows you to coax, for example, a 3 ft piece of binding to ft an edge 3 ft 3 inches in length.

The stretchyness allows you to bind around curved corners, scalloped edges, or a round quilt (mug rug or table runner) easily and smoothly.

Matching patterns: if your binding has a printed recognizable pattern, cutting on the bias allows short pieces to be matched and connected with less attention to whether or not that print is recognizable. On a small piece, a too-bold, too distinct pattern on your binding could be a distraction.

These are my reasons. I've used straight-grain binding with both success and frustration. When I'm working on a very stable, perfectly squared quilt, then straight grain binding is okay.

Traditionally, other ways were used to bind quilts, including straight bindings. Bias bindings wear better and longer and it is easier to make a nice mitered edges at the corners. Aesthetically, they are more appealing to me. They just take more fabric to construct and require a little more skill to apply.

Patricia Cummings, quilt historian/ certified master craftsman in quilting

When making a quilt for competition, what would a judges critique be on bias vs straight?

I only use bias binding on quilts with curved edges, otherwise its straight grain binding and have never had problems with them wearing.

I use straight, length of fabric rather than WOF and I connect it with bias seams. Works great, although I haven't done any curved edges.

I always cut my binding on the straight of grain. With straight edges on a quilt there is no reason to use bias binding.
Bias binding would be for curved edges which I never do.

Bias binding is only necessary when edges of the quilt are curved. If all edges are straight, cut fabric on the straight of grain. I've bound straight edged quilts with curved corners. In that situation, piece bias sections into the binding at each corner location so the fabric curves smoothly.

Sandy

I used bias only because my Grannie did so that is the way I was taught. I still have a roll of binding that she made that I haven't used. However, the seamtress in me asked WHY so now I use straight grain. Easier and faster to cut. All the old patterns I have say to use bias and I have no explanation as to why.

i only use bias if the quilt has curves, but for a regular square quilt straight of grain is fine

Bias binding has "give" and makes sewing binding on curves easier and neater.