Corner sinks are not exactly uncommon. Every cabinet manufacturer has a corner sink cabinet or 3 in its catalog. Length along the walls seems to be most commonly 36" or 42". I don't know the answer to your questions about efficiency of space usage.

I had a corner sink at my old house (don't mind the disaster - I was packing to move to new house):

And we have a corner sink in the new house. When we looked at the new house, I was shocked to find a corner sink - it was like it was meant to be, just for me!

I like corner sinks, but they do take up more space that way because of the angled cabinet. Still to me it's worth it if it gets you more contiguous space for prep work.

I'm thinking about an eat-in kitchen and I think the unavoidable sink of dirty dishes is less in-your-face when it's back in the corner like that.

Deb, your new kitchen is beautiful.

My mother-in-law has one she hates, but I think it is largely because she is staring at two walls, no window like your picture.

I think of them as "the sink of last resort" because I'd rather have the sink in almost any location but the corner! They are OK in a small kitchen, but they don't really "save" any space. If you want as big of a sink in them as you can have on a straight run, they take up more space than the equivalent straight run location. They are a royal PIA to have if you need to have more than one person in the kitchen at a time. And they are often not done well, and have the DW right next to the sink, giving someone who is loading the DW barked shins and no place to stand.

we have a corner sink and it's just as described by GD, the dishwasher is right next to it and if the door is open you are basically trapped at the sink. Also it truly is a one person sink as there is no room to scoot over if someone else needs a little water or such

We haven't started our kitchen remodel yet but I can tell you that I hate my corner kitchen sink. For one thing I can't reach behind it to even clean it! It is entirely too large since it's a top mount. I will still have to have a corner sink because it will require too much change to move it but we are going to take down the raised bar and have a bar that is level with the counters. That way at least I can clean the darn countertop.
I'm hoping a single undermount sink will also give me a little bit more space on the right of the sink. When we bought the house I thought well that corner sink might be nice...I was wrong.
I think it all depends on how much counter space you have and whether or not you have a window or open space.
I can't wait to get started on the remodel but it's at least 2 months away.

I'm likely moving my sink to the corner in my reno. I have a small kitchen and that move will maximize the amount of counter space between the sink and range. We're planning a 39" corner and will have the 15" trash pullout between the sink and DW.

I currently have a corner sink like the one in the first picture, except that it faces corner windows. My dishwasher is right next to it and I HATE IT. This configuration (here when we bought the house ten years ago)is actually the basis of my kitchen reno. I can't begin to explain how ill-functioning, uncomfortable and awkward this is.

The new configuration will be like the second kitchen picture and I'm excited beyond words. There will be a cabinet between the DW and the sink so you can actually stand in front of the sink and load the dishwasher.

Also (and this is really big), instead of the AWFUL right/angled sink and cabinet, the flat fronted new corner cabinet will actually allow you to stand facing a regular sink(as in the second picture).

As for wasted space behind the sink, that is just not an issue for me. I'm thrilled that I will actually have a space that will function well.

For me, the corner sink is not the issue - it's the right angled corner sink in the right angled corner cabinet with a nine inch space in the corner to stand in to load the DW.

We are installing 2 corner sinks so we get better cabinet space. To mitigate the dishwasher problem, we are putting the dishwasher one cabinet over.

We have a corner sink with the dishwasher flanking it, and when two people are trying to do something around there at once it's a traffic jam. I'm not sure if there was a better solution for this space, however.
One other thing: keeping the deep space behind the sink clean is an issue (long reach, then with cabinets above).

I currently have a corner kitchen sink and hate it.

Our setup looks very similar to the 2nd picture linked above. Our corner sink faces too small (22") windows. We do have the DW nearby but there is a 16-18" trash pullout betweeen the sink and the DW so there really aren't any issues when the DW door is down. That aspect of it works well compared to hearing some complain about the DW being right next to the sink.

What we hate most about the corner sink is how awkward it is if a 2nd person needs to use it to rinse off something or wash their hands. There just isn't much room for two people to maneuver in that corner. We don't have a 2nd prep sink so that might contribute to our hate of this corner sink alot.

My sister has a corner sink and hates it, too. It's so hard for two people to get to the sink, plus you are blocking drawers when you stand there. Her dw had to be placed a little farther over to make space to work at the sink and now she has to deal with drips from the dishes that. are loaded.

The space behind the sink is kind of a dead zone. Anything pushed back in that corner is out of easy reach. I'd never have a corner sink unless it was the only option.