Delete vertex with [d] key & toolbar icon in more editing tools
Right now if you accidentally add a vertex while editing with a tool such as Reshape, you have to R click very precisely and without moving your mouse on the point you created and choose Delete Vertex.
Sometimes, it gives you the wrong menu, which means you have to try multiple times to get the menu option to show up.
This is especially cumbersome when trying to remove multiple vertices without losing or ending your drawing. It would be more consistent and much easier if the toolbar had the Remove Vertex option on it like the edit vertices tool and if the [d] key worked for activating. It's just really strange that there are two different ways to remove a vertex depending on what tool you're in.
This is how tools work in Adobe Illustrator - you can use [-] to quickly remove vertices while drawing.
Yet another type of menu from R clicking on a vertex:
Your request makes sense but I do want to clarify why you are seeing different context menu items, or at least why I think you are based on the screenshots...
In the original comment, second screenshot. The Direction-Direction constructor is active. That context menu shows when the constructor is in progress as that is the context menu for that that context. Need to esc or finish up the constructor to get the desired vertex editing context menu.
In the second comment, the Trace constructor is active. I don't think the active constructor is important though. I think you right clicked very fast, before vertex editing mode kicked in.
When cursor looks like this, you will get the Trace (or active constructors) context menu
When cursor looks like this, you will get the vertex editing context menu
Additional piece of information, you can toggle on/off mid-sketch vertex editing from the Edit toolbar
Hopefully this additional information is helpful.
-Jennifer