When initially adding a curve for local position or local scale, creating a curve will make the entire curve visible with a single key. However, when adding a curve for local euler angles baked, adding a curve does not visibly show a curve until a second key has been added to the curve. See attached video.

Repro:
Select an object with an animation
Add a curve to local position
Observe a straight line for the curve is drawn
Delete it
Add a curve to local euler angles baked
Observe that a key is created but no visible curve is shown
Add a second key later in the timeline
Observe the curve appears when the second key is added

Result:
Creating a curve on local euler angles baked does not initially show the curve, making it difficult to double click to add another key