This was the way I was taught as a kid. It was my job to do the hemming on an old treadle machine!
Never used binding until after I retired and started taking quilting classes.
Now a days I choose the method which works best for the quilt.
When I use fleece, minkee or a nice flannel for the backing, I will hem the quilt, otherwise I use a double fold binding.
For hemming:
I will trim the batting even with the quilt top.
I will trim the backing two inches all the way around.
I will then take my long ruler and line up the 45 degree line even with the quilt top at the corner of the quilt.
Making sure the side of the ruler is 1/4 inch past the top of the quilt corner (seam allowance) I will slice off the corner of the quilt.
Then I will pull the sides of the backing together (right sides together) and starting from the corner sew a 1/4 inch seam half way and backstitching to lock the seam.
Then I will trim a little at the corner to reduce the bulk, making sure I don't cut the seam thread.
Then "pop" the corner.
This makes a nice mitered corner and reduces the bulk on the corner.
Repeat for the other 3 corners.
Then I tuck the rest of the hem down and stitch around the quilt using a quilting foot.
This gives a nice one inch hem all the way around.
Fleece, minkee and flannel are tougher than the cotton used in making binding. The quilts that I did this to several years ago are still holding up really well.