It looks like the Inset tool is making it WAY TOO inserted. If you are completely sure the vertices are welded together, the size of your mesh may have something to do with. You can either resize it or change the values of the Inset tool manually. When you hit Inset, try setting the value to something like .001. Then, work…
I did a quick test on Max and a clean inset wont produce that error. By change you got a double vertex on the top tip? cus i got that error result when i add small chamfer on the tip. Try to clean up your model and make sure no overlapping verts.