I don't think anyone can answer the 'Why', outside of ZOS - and I don't remember they say anything about that. Well, nothing that really struck me, but don't trust my memory too much ( I don't ).
I guess it kinda boil down to having a kind of currency, Luminous Ink, being needed and consumed each time you change a scribed ability ( which is, from the beginning, a bit of a weird and not really great idea in my opinion, but anyway ). Saving scribed abilities in the armory could be a way to bypass the necessity to pay Luminous Inks.
And their could be more problems about saving scribed abilities in the armory, I don't know, but obviously ZOS is still struggling with technical efficiency - it's not an attack against ZOS or a wild guess, it is something they themselve recognize, hence the recent Vengeance test - and maybe implementing a way to save scribed abilities with the armory is difficult, or can lead to difficulties.
Anyway, it's a shame that we can't, especialy when scribing came at a time when ZOS were boasting about QOL changes. It is sadly telling.
We save gold by using the armory to respec skills. Sometimes a lot of gold (50g per skill point invested, and I often have over 400 skill points invested on my main = 20k+ per respec). The gold cost in Ink saved with the Armory would be a fraction of that by comparison, since Ink is so cheap now.
There is a big technical difference in the way that Scribed skills are stored compared to non-Scribed ones. Scribed skills seem to use skillIDs, but there’s also a lot more going on in terms of how they store their information, so it isn’t as simple as the 1:1 relationship between skillID and non-Scribed skill. ZOS would have to do more work, as I believe they’ve acknowledged, to get Scribing to work with the Armory. It isn’t like it’s already in place but they’re holding back to prevent us from saving on Ink.