It would come down to the problem of "Not created"
There's a few ways to "Make a pickaxe" and the BLACKSMITH can hold every one of those ways.
But Customers will only buy one specific way.
2h grip + pickaxe head - and it will inform you "You created a (metal tier) pickaxe!"
The other ways won't say that, but you can still equip them personally.
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Alternative Reasons it may not be functional.
-Assembled Pickaxe correctly, but didn't sell it before saving and reloading
-Rare- Assembled and didn't save/reload but 5-30+ mins later no item that was crafted could sell anymore.
(Fix for both)
Take to anvil and smack them with hammer - disassembles allowing you to reassemble (or partially rework after reheating)
(Prevention for both)
Don't Fully Assemble the parts until a customer wants it.
If you never complete the item - saving and reloading will never break the item, meaning you'll never have to disassemble and reassemble it, equally so for rare/random break.
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"You created (Metal tier) (item)" is true for all customer purchase items.
For example
Combining a Polegrip + 2h guard + Large Blade (Greatsword blade) = Polearm - It will inform you that you created a Polearm, and customers will buy it.
Combining a Polegrip + small hammerhead will also make a polearm (variant 2) - it will inform you.
However.
Combing a Polegrip + 2h guard + hammerhead (any) will either not combine at all, or won't inform you "You created a polearm" and customers won't buy it as a result. (I can't recall if it doesn't combine or doesn't inform you and still lets you combine)
You /can/ combine a polegrip + 2hguard + small blade (dagger) and make a polearm (spear/variant 1)
But /can't/ combine a 1h grip, guard and small blade, and won't make a dagger when you do so. (won't inform) - customers /won't/ buy either.
I can't remember if you can combine a polegrip and either axe head, but At minimum, they won't sell. (Halberds = no go)
I believe I made a point about using 2h grip and small axe head for player axe - which, if I recall right, the Player can equip any small axe combination much like any pickaxe combination - but 2h+ small axe =/= anything and customers won't buy it.
Player can't equip large axe head if I recall right
Player /can/ equip large hammer head though, If I recall right... I might be recalling wrong, Though, Only if its not a greathammer, I think, If I recall right. - I could be wrong here, again, I did my combination testings a while back, prob more than a month now. - and I don't recall if grip+small head worrked, it might also not work because it makes something that isn't a hammer specifically.