I am no friend of too fancy and tricky functions. So I am all with Gene here. If you want to delete an arc, delete it. If you want to trim a line trim it. But don't use some other function for it. There may be users who will appreciate it, but there will also be users, who don't.
There is something fundamentally different between point-on-object and coincidence. In the general case point on object means that one line ends there, while the other doesn't; so there is something which can be trimmed. Coincidence means the both coincident elements end there and nothing is to be trimmed.
The wiki may describe things wrong, then either the wiki or the implementation should be fixed. I hope we can agree that we cannot derive from this, that anything coded is questionable.
Errors can in many cases be handled more gracefully, and perhaps this should at most throw a warning. But it shouldn't do anything with the sketch.