Interesting. Maybe not 100% the associations I'd have made but close enough for rock and roll.
Were it me, for game-play sake I'd split out elemental energy such that different colours would have more access to damage-dealing. Cold/ice would go to White, for example; electric/lightning to Blue; light to Yellow; while fire, heat and radiation would stay with Red. Not sure where 'force' would go.
Just for kicks, as it's not been mentioned yet, sonic magic would go to Red to make up for all the elemental bits it just lost. Come to think of it, I'd also split out the elemental matter bits from Brown: Blue gets water, Grey gets metal, White or Orange gets wind/air, Red picks up sound to go with fire and maybe Black gets earth. On this, Brown would become redundant and disappear; or if it remains it becomes the catch-all generalist area for things that don't really fit anywhere else.
I'd split out psionics into their own discrete system* (some people don't like sub-systems but I often find them highly useful) and move illusion into Purple as illusion overlaps greatly with mind magic anyway. Grey would get wild magic along with raw magic; though particularly if it keeps illusion I'd drop Grey as a designator and replace it with Rainbow or All-Colour.
* - in part to make psionics modular enough to be fully optional: a DM who doesn't want them can just drop without causing knock-on balance effects elsewhere in the magic system.
There's various minor types of magic that'd need to be shoehorned in here somewhere (or just dumped into Brown the catch-all): written magic (including scroll creation), dream magic, summoning and-or banishment magic, and - perhaps most importantly - travel magic.