The actual reality of why they don't do it is because they'd have to effectively re-design how the glamour system even works on the coding front. When you 'glamour' something, the code is basically assuming you've 'equipped' the piece, which is where the issue starts. Because its using the equip system, the coding restrictions on what job can equip what gear kick in. For them to make any piece glamorable by any other job, they'd have to re-code the glamour system and figure out a system that de-couples it from the equip system's coding; since making any piece glamourable by any other job in the current coding system would literally mean changing every piece to <all classes> for the equip requirement, which introduces balancing issues (where you'd want to equip as much tank gear as possible due to increased defense.)
Even if they managed to do so, it wouldn't prevent them from re-using assets. Take a look at the Anamesis gear being re-tools of the Shire gear of the same job type the shire gear was for without job mixing. Also the forgiven's gear all being re-used from World of Darkness gear of the same job type as before without job mixing. It ain't an issue of using it as an excuse to re-use gear; its literally because they don't have the time to re-tool the glamour system in their short dev patch windows, or don't see it as an issue.
'white mages using axes' is basically the usual non-technical answer they give to any technical question, since half the terminology they'd have to use to explain why its not going to happen at the current time would fly over 90% of the playerbase's heads.
