Bias binding does wear better. It's actually as easy to work with as straight-grain ***IF*** you starch the fabric heavily before cutting into strips. I use a 1:1 solution of Sta-Flo liquid laundry starch and water, "paint" it on the fabric with a large wall-painting brush until the fabric is saturated, toss in the dryer, then iron with steam. Heavy starch stabilizes the fabric so much that the bias becomes easy to work with. (Doesn't mean you can mishandle it; just that it comes our requiring only about the same amount of care as a straight-grain binding does.)
I do like bias bindings on baby quilts for the reason cited -- all the extra machine washings they get.
Edit: Heavy starching might not work well for curved edges (because it becomes more difficult to stretch the edges). I have only ever used heavily starched bias on straight edges.