Why this fear of bias edges?
 

I'm not understanding the fear or caution expressed when bias edges are mentioned in anything. My first quilt was Ocean Waves and I used the disappearing pinwheel blocks with my 4-Hers. My view is that the stretch of the edges allows fitting opportunities.
If pressing is done carefully - pressing not ironing - and pinning is done, then the blocks can be completed satisfactorily. I'm currently working with blocks that my members have done for a group quilt. So far I've only had to reconstruct one block and I'm still not sure what the member did that was wrong. And I have had to add extra strips to the block edges because the some of the blocks vary in size - but I think that the quilt itself will be lovely. (I'll post when it's complete!)
But then I am not a traditional quilter. The idea of cutting small pieces and then sewing them together gives me hives....

Long may she wave. I have had many quilts go wrong with bias edges. Of course, it's due to me stretching the fabric by either sewing wrong or pressing wrong. The only time I really worry about it is in a show quilt. Usually, I do like you said, just quilt it out. Since I make throws, I figure no one is going to notice because they are rarely folded and placed where it would be noticable.

In some ways, bias edges can be your friend because you can manipulate them a bit if you have a lot of seams to join. You have to do it carefully, of course.

Watson

I think the fear or caution is noted for inexperienced quilters, of which every single one of us has been at one time. I know that I struggled and was frustrated with bias edges at one point, and I did not know why I couldn't get my seams and points to match. If someone had pointed out that I was dealing with bias edges and the possible consequences of not managing them properly, I would have been a lot less frustrated!

Now that I'm more experienced and knowledgeable, I agree with Watson - bias can be your friend. ;)

after I figured out that starching the yardage before I cut solved any problems I've had not had problems.

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!

when I was a newer quilter, I would press so aggressively that my pieces would get distorted. I don’t have too many problems now with them as I’m more careful.

Bias can really mess a block up. I cut out a lot of big hexagons then decided to cut them in half. Big mistake. BIG. I had no idea which ones had the bias in the middle. Nothing fit back together.

I'm another that got most of my sewing experience with garment construction before moving on to quilting, so bias does not give me any fits. I do have to pay attention if I'd dealing with bias, but I don't worry about having a bias edge if I cut a square in half or something like that.

I've got a lot of sewing machines, and some really do not deal with bias very well. I often wonder how much of the difficulty some people have is because of the machine they are trying to do it on.