The workflow to move a sketch created with the rectangle command is even more problematic.
And this is not an edge-case. More like an origin story... Certainly, for most users on their journey with your product.
If the starting point for the rectangle is at the origin (of the drawing), you can right-click and see the option to Delete Coincident.
Or, (more likely) you will click the dot on the corner of the rectangle and see not one but two coincident constraints. But which one to delete. (Correct answer: the one on the left.)
For a new user, the presence of two coincidents at the corner raises a deep confusion. Why two? (I thought I was just drawing a rectangle.) “I get that one coincident is between the ends of two lines of my rectangle; but what about the other coincident? What’s that coincident to?”
In any case, the user boldly deletes the first coincident, catches a lucky break, and then proceeds to move the box and then Stop Sketch.
But what's that ugly red circle visible at the origin, even with the origin turned off? Right click on it to find it in the browser and it's confirmed that it's associated with the sketch. So go back into the sketch, click on it and see (bottom right) it's a sketch point somehow left over from the rectangle... which nonetheless still has its four corners intact.
Hit delete, but the mystery dot is still there. Right click to delete using the helpfully provided delete option, which then asks you to select the entities. Click all you like at that red dot, but the Move/Delete dialog select doesn't want to know anything about it.
So, in this user story, we have a few problems: Whatever the red dot is, it's not a mere Sketch Point like all the other boys. It's more like an "App-Created Sketch-Embedded Immutable Intersect [i.e. reference] to the Drawing Origin". But it needs a name and identity within the context of the owner sketch; its identity (surfaced in the GUI and documented application concepts) needs to be discoverable; and, the user needs to be able to know how (and be able under many circumstances) to operate on it.
A similar challenge arises when a sketch is started at a user-created-point (such as at the intersection of three planes). There, after deleting the automagic coincident and moving the rectangle there is a point left over that, when clicking on it, it shows an obscure icon that looks like a mortar board from graduation ceremonies, one that does not appear in the Constraints list. Turns out it is an Intersect. The good news: this time it comes with a context menu that includes "Break Link". (Break that and the icon indicating the Intersect curiously remains until you move the point. So it wasn’t just a relationship. “Was it an actual object, the user keeps wondering, or more like a spot on my glasses?”)
Solving the problems in both use cases requires promoting these automagic sketch origin constraints/intersections/locked links/snapped to items/contingent correspondences (pick a name/concept) to first class citizens, and making discoverable what is on the other end of the connection. When I do a long left click on a corner of my rectangle, I should never see three “Sketch Points” under something called “Depth”. One of them needs a new identity. Furthermore, you could add a tab to the same control and call it “Intersections” or “Links”. Later, you might want to enhance this control to enable operations on these items (most notably, Break Link), and to enable tooltips that indicate to what object an Intersect is linked. Check out how Excel enables viewing various properties of links in a workbook that refer to other workbooks/files. Or how Visual Studio enables control-clicking on a reference to take you straight to the definition. Or how your team is now handling Insert-Derive. Object references are essential to tooling for complex compositions, but the user needs to know what's on the other end as well as the nature and status of the relationship.
Alternatively, you might want to go easy on users by enabling them when they say they want to move all 8 (or even 9?) points in a sketched box using the full ceremony of the Move/Copy control. (Trigger confirmation dialog boxes about link breakage all you wish. Trust but verify.)
Finally, more broadly, you might want to enhance your usability testing. Gather lots of video of new users during their first 20 hours with the tool that includes an audio “director’s track” with them later explaining what they were struggling with. The product is already superb but there is some work to do in making it more usable for new users.