Generally it'd need to be a 'theme' of some sort, with the theme getting broader the more developed it is. One of my favorite canon Forger techniques is from the first book, where one of the protagonist's rivals has a Forger technique that's literally just "make a brick, and then I physically throw it at you", which is treated way more seriously than the comedy beat that it sounds like. The character's only Iron, and not actually that skilled at the sacred arts as far as the wider world of Cradle would consider things, and his technique topped out a "makes one(1) brick per use". The inverse of this is Mercy's Strings of Shadow technique, which Mercy has used to make bows, arrows, restraints of all sorts, bind herself to something and then shorten the string to yank herself around... it's one move that can be attack, defense, mobility, and general other utility: she uses it to do even things like stand up a chair that had fallen over so she doesn't have to look away from something she's focused on.
Right now, we've already seen Keras grow replacement axes, although they've used that for blunt training things instead of an equivalent weapon, but, yeah, a Forger technique to create "generally a hand weapon" or "specifically an axe" is fine. More advanced sacred artists often start with "a really big version" as a flashy opener when they have one of these techniques. It's one of the techniques we see King Seishen Dakata use in "Underlord", in fact: he Forges a huge sword as an anti-flying-ship move. Keras could certainly develop a Forger technique in the sort of direction you both are talking about, but there were two vote options so far about combining their current Forger technique with axes and they weren't taken. I have pages of other shiny thoughts that might grab even more attention than this type of new Forger move.
...More seriously, though, generally learning a new technique is a fairly serious thing, so the real concern really is opportunity cost. This proposal is a good one, but it might or might not be worth it to develop like this. It's almost certain to show up as a vote option at some appropriate point, though!