You will need 1332 bag/bank space to hoard those 4 colors item [white, green, blue and purple] 9 different traits and 37 different pieces (21 armors [heavy, medium, light], etc) sure you could destroy the white as soon as you don't need but u will still need 999 slot to stock them... and a few double of some key pieces for your 2nd and maybe 3rd companions etc...
who is the genious that think that its fine to use player inventory to store them...
easy solotion would have been to drop companion augment glyph (different color, different traits) 4 color 9 traits = 36 total not 1332????!
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then we could have use the companion gear vendor to buy one white pieces of gear (one of the 37 different pieces) and augment it with the companion glyph vendor should supply the white color augment traits for initial companion setups...
sorry for my english but 1332 items for companions is a freaking tons of item to keep in our bags, or another freaking tons of years of grinding for each pieces
and your clearly said companion won't have their own inventory
please reconsider its not to late