I was trained as a seamstress and bias edges can be an asset or a disaster depending on when and how they're used. Curved patterns are going to have some biased edges, so they require more basting and trimming. Not cutting basic squares and triangles on grain can cause a lot of problems in finished quilts as when the fabric is manipulated in any way they can stretch and sag. This makes them difficult to square.
When I was in college I worked in the theater costume shop. One of the designers insisted on cutting her medieval gowns out of stretch velour on the bias. I was appalled and told her that the gowns would be unwearable after one performance. I was right. Before every performance, (including the first one because she told the costumers to hang the gowns), myself and another seamstress had to sew the actresses into their costumes because they had grown in all directions. It was a disaster!