I'm a pretty firm believer in there's more than one way to do most things. But, that being said, "most" vintage and antique quilts (especially prior to 1920) had narrow bindings of straight-grain fabric often of a different print/color from the rest of the quilt. Indeed, Barbara Brackman, quilt historian, once said she had seen only one out of literally hundreds and hundreds of pre-1900 quilts with a bias-grain binding. Curved edges came into vogue in the 1920s and 30s and needed bias grain for those curves.
Oddly enough, quilting as a craft/art was a bit "lost" in the mid-1900s, after the heyday years of the late 1920s into 1930s. Many quilters of very late 1970s and early 1980s were either newbies or "rememberers" of their grandmother's work. Many who had mothers who were young women in the 1940s had to virtually reinvent the wheel to quilt.
Most of us at that time remember template piecing, not strip piecing, and turning the binding from the backing fabric to the front for binding. Many of the quilts had "modern" polyester batting that was thicker than nearly any generation before us had used and therefore had 'fatter' bindings.
It wasn't until 1980 that the rotary cutter, which had been recently invented in Japan, became available in this country for the garment industry, for instance. Quilters quickly found the new invention and it sold better in the US than anywhere else in the world!
Personally I'm SO glad I was fortunate enough to begin quilting with the forerunners of the "speed-piecing" method of quilting like Mary Ellen Hopkins. Because, even though there were few decent quilting books available in 1981-83, she wrote a magnificent primer for the new generation of quilters/fabric artists that truly set us free to think outside the original box and do things a different/better?/ faster way.
We can do most anything we please these days! We've come a long, long way, Baby!!!
Jan in VA