There is no law that says a binding has to be a certain width.
I like wider bindings (I usually cut them about 2-7/8 inches) and I am more comfortable using bias binding.
For me - pinning the edges together first to make sure that the binding lays "right" and then machine basting the edges of the binding together with a longish, narrow zigzag stitch is an important step for me. Otherwise, one edge would sometimes get away from me.
I trim my quilt sandwich to the finished size and also sew the edges together about 1/8 inch from the edge.
My reason for doing this is - I only have two things to match up then, instead of five.
I usually do a test run on a scrap sandwich using the same batting, etc. to verify settings and widths before i go very far down the road.
As far as bias binding using more fabric than straight cut binding - it takes so many square inches of fabric no matter which way it is cut. - okay, there might be a little bit of scrap at the corners, but not very much.
If I did use straight cut binding, I would use whichever way had more stretch - which is usually the width of fabric instead of lengthwise grain.
I did use T-shirt fabric once for a binding. Turned out great!