You can find details for the suggestions in the spoiler blocks below.
Issues with the current system- companion gear is often worthless (even for collectors)
- only very few pieces are interesting for companions or guild trader
- green and blue pieces are used relatively rarely
- many destroy them or sell them to traders for gold
- unlike plunder/trash items the gear is worth almost nothing at the trader
- cannot be marked as junk
- cannot protect it from accidental sale (no locking)
- unlike normal equipment the pieces cannot be deconstructed
- some people post them for tiny sums at the guild traders
- others flood guild banks with them
Intro
Suggestion 1: Merge - random
Merge pieces of lower quality gear for random higher quality gear (my preferred suggestion).Thoughts:
- 5 pieces of the same quality could be merged into 1 random higher quality piece
- only small amounts of pieces should be required, because the gear does not stack and it already takes up a lot of space
- RNGesus compensates for the small amounts with luck being necessary to get the desired outcome
- gold or a reagent could be required for the merge
- "bound on equip", will make it valid for resale
- even green quality gear will be sought-after
- no new material type necessary, the gear is the material
- no lvl barriers for players
- gives people more options for farming companion gear
- merge could be done at crafting tables
- gear could could be exchanged at traders for a random container (+fee)
- could even be done by a companion in the dialogue in the inventory using a reagent
- costs for reagents or fees would take gold out of the cycle (goldsink)
- takes items out of the cycle, through merge/exchange (x:1)
- RNGesus delays being able to farm the "perfect" gear to fast
Example for merge costs (with slot and type constraints):

Type could be armour (light, medium, heavy), weapons and jewelry; slot could be "Head" or more limited "Head, heavy"
Example for a merge using a crafting table (no type constraints):

(5 blue pieces selected, 1 random purple piece created)
Example for a merge using the companion dialogue (no type constraint):

(companion gear in the inventory: 13x green, 2x blue, 6x purple, 3x gold. After picking a dialogue option some kind of trade or deconstruction window could open to let you pick the pieces)
Suggestion 2: Crafting - targeted
Deconstructing gear into raw material. This could then be used for targeted improvement or crafting. The randomness is gone.Thoughts:
- new material type necessary (because not all players are LVL 50)
- could drop only from deconstructing companion gear
- but new material would take away inventory space, if you don't have ESO+
- alternatively it could use transmutation crystals for trait changes
- new players don't have good access to crystals
- existing material could be used instead, that is player lvl neutral (like furniture materials)
- new trait material would necessary
- at a pinch existing trait material could be used, with a different effect for companion gear
- required raw material should be 10+ times higher than with suggestion 1 (because randomness is gone and materials can be stacked)
- if the system does not require crafting skills, then the gear can be "bound on pickup"
- if it required crafting skills, it should be "bound on equip"
- takes randomness almost completely out of the equation, like with crafting overland sets
- companions might get equipped too good too fast, if material requirements are too low
Suggestion 3: Drops/Quests - random
Higher drop chances for higher quality gear. In addition there should be quests / enemies, which have an increased chance of granting a specific high quality item.Thoughts:
- purple gear should drop more often
- some pieces could be gained specifically from quests (0 random or higher chance)
- specific world bosses could drop specific pieces
- daily guild quests are good candidates for a higher drop chance for random golden gear
- it would revitalise some overland zones for a limited time
- guild ranks could be used to unlock purchasable gear
- companions might get equipped too well too fast