I can image a pipe axe easily. If you have the tools to craft pipe weapons (you would need at least a metal saw, a rasp and a drill) then a pipe axe is trivial:
View attachment 20656
The two holes are for a metal pin.
Look at how stone axe already makes lower quality levels of iron axe obsolete. If you just add further tiers inbetween already narrow tiers you just generate more content to be ignored. The only "hole" to plug would be in endgame but that depends how far TFP wants endgame to last in vanilla. They already indicated a few times that vanilla last long enough for a beginner and the minority of players doing dozens of playthroughs can get their fix from mods.
Sure, but what has that do to with the tier they are supposed to fill? You are free to call them whatever you like, they are the tier0 weapons corresponding to tier0 tools and tier0 melee weapons, all easily optainable at start and craftable without schematics. Any label you put on them is just for immersion.