My first object is a curve (not a polyline) and has what humans would call 2 corners. CC declares that it has one corner, then messes up rounding it. I could see have zero corners (since it’s a curve meeting a line), or two corners (the object is perfectly symmetrical). One corner is just wrong.
If the only working use case for the corner tool is “two straight lines meeting”, then it should enforce that instead of giving random answers.
As Tod pointed out, there are two tools for this — when the Corner Tool with control fails for me, I sometimes remember to instead duplicate it, apply Fillet All to the duplicate, then draw lines so that I can then use Trim Vectors to cut down to a series of lines and Curves which can then be assembled into the desired shape.
That’s what I ended up doing. The ‘outside-then-inside’ approach was an experiment to see how curve-vs-polyline affected things. Turns out both are broken, but in completely different ways.