IMHO, lengthwise grain is fine for binding a square or rectangular quilt, and especially for smaller quilts. No problem. It is my experience that the larger the quilt, the more easily the binding will go on with either a cross grain or a bias cut binding. Of course, with any edge that is not straight, you'll want a bias cut binding.
And, of course, the above all depends on the experience of the quilter. You do what you're comfortable with, and what works best for you, naturally.