Because the pair of distinctions chosen makes sense in some cases and not in others.

I provided two examples in my comment above.

I don't see any examples in your comment.

I might be engaging a troll, but I'll ctrl-c ctrl-v.

"It may be that libertarian/authoritarian Left is a meaningful distinction in some contexts and not others; or that authoritarian Left/Right is a useful categorization for some purposes, but not for others."

Seriously, I am not trolling. Those are not an examples, you're just re-iterating why you think the quadrants are inappropriate. My question is what are some specific examples of "contexts" in which lib/auth left/right is NOT a meaningful distinction?

From where I sit, the quadrant is the least bad way to classify and categorize ideological views. It's certainly less lossy than categorizing on a single dimensional left/right spectrum.