I note the York museum listing mentions the slotted construction. The axe blade does seem to be slightly distal tapered, tho the hook isn't. It doesn't look like it was cut from rolled sheet, it's forged thin. The screw is hand cut, not machined/ lathe cut, maybe it was dis-mountable for storage/transport? The sharpening could have been a personal preference of one of the previous owners, i gather they were not usually sharpened. The hook is more butterknife sharp, while the axe and spear is dangerously sharp.
The Royal Armoury ref. indicates the spears were threaded onto the sockets.
A slightly better defined photo of the head: I added the arrows to show the screw joint and the flush rivets on the axe/hook fastening.