Are you asking single or double bias binding...
As for binding a quilt I do the french straight bindind unless it is curved then I do a bias french binding.
The trick is you never want to use single fold for you only have one layer of fabric on the fold outside of the quilt and yes either way srtaigh cut or on the bias it will wear many times faster.
Mostly the bias maker is for garments and crafts. Or home decor. I love working with bias... it is most wonderful in appliqued stems, and wonderful for baby bibs abd hot pads.
And as I read back yes I will cut a stripe on the bias just to get the effect I prefer sometimes to .