You don't lose the dye like Chameleon extract. There are eight slots dedicated to the prismatic dyes. Those slots are saved similar to keepsakes and won't change unless you override it with a new dye after filling up all eight.
• You have your basic 16 colors (non-dye).
• You have eight empty slots for prismatic colors.
• You can buy prismatic dyes to save colors in those eight slots.
• You can re-use any of the prismatic colors on any recolorable outfit.
• You can overwrite any slot with a new dye like the reclaim option on Keepsakes.
Assumptions
• You can change any prismatic color with a new dye before saving all eight slots.
• They will not be HSL compliant since it's not the same as the existing color pickers.
• You will be able to see what the color is before setting it like the chameleon extract.
• You can re-use any of the prismatic colors on any recolorable outfit.
Just that is worth it imo if you really want it, not like it will cost you fortune, as well as being able to pay for pretty much anything with GP in game via bonds.