Are people specifically breeding for "pet" traits or is it that they aren't breeding for any traits when breeding for pets?  I would shy away from the first type, who knows what their idea of a "good pet" is and as for the latter, you can get quite the firecracker.

Depending on the type of breeder. The ones specifically breeding for pet traits are breeding down. The ones that aren’t breeding for any traits tend to produce crapshoots in general. You usually end up with a wide range of random traits you can get in the dog. Breeding specifically for pet traits does a disservice to the working dog in general. Not breeding for anything in particular could be better or worse. You’d probably still end up with dogs a lot closer to the intended function.

None of those comments are absolute rules, they are observation of people other forums.  It seems from what I see locally, that showlines are easier, and of those ASL and pet lines seem to workout better for inexperienced owners.  Yes, if someone gets a WL with a good temperament it might be the best dog they ever have.  Most WL breeders seem to select for driveyness and intensity.

Corvette vs a Prius.  Yes.

My fear biter was a pet line.  He looked just like a Royalair dog, so he was either from that kennel or a similar breeder.  He had a weird temperament for a German Shepherd.  I was fostering and the longer I kept him the clearer it became no one was going to adopt him, and he was so attached me, we decided to just keep him.

I’ve seen dogs advertised like that.  One kennel that was highly recommended for pets had a female that was a “good producer.”  She was kind of lumpy, her coloring was washed out but I called them anyway because of the rec. the woman told me she had a list for that dog’s puppies for the next three years and was not going to breed her more than 3 times, then retire her.  She said that dog had the most popular of all her litters.  I was interested because her sire was Vom Kirschental. I did not want a puppy from her after hearing how and why she bred.  They were clearly all pets, and she was intentionally making softer, quieter, slower dogs than her male’s line.

That diagram really shows the differences.  I would love to see ASL thrown in there too to see where they lie.  It would also be helpful to see what traits those genes represent.

People are experimenting with crossing half ASL and half WGSL, hoping to get a better structure.  If you take an extreme slope and mix it with a roach, do you get a dog with more moderate lines or do you get a dog with its butt on the ground and a roach back?

I’ve seen some decent WGSL/ASL mixes. Still more curved in the back than I like though. 
 

As far as pets go, I think in some cases traits that make a good pet aren’t always selected for when other priorities get in the way or good trainers are raising the dogs. And people breeding just pets are usually just breeding any random two dogs together so they still aren’t selecting for traits that make good solid pets. 
 

All the amazing GSDs I’ve met were all just random pet bred dogs. It was definitely the temperament of those dogs that got me interested in GSDs. But I’m not sure how hard it is to actually find that dog with good breeders 

If an excellent breeding happens on accident, it’s hard to duplicate without the same dogs,