@CubicsRube, I had a similar idea. My "solution" was actually to look for another system. This is not to say that it can't be done in 5e D&D, because
I think that it can, but, rather, I personally preferred looking to something similar enough to D&D where this would more lucrative or where the pre-existing magic system made it somewhat easier.
In particular, I checked out Shadow of the Demon Lord, which groups its spells into more thematically similar magical traditions: e.g., Time, Fire, Primal, Death, etc. It was easier for me to then look at those thematic traditions and group them together in ways that corresponded more approximately to the Magic Color. Similarly one could do this with the AGE System, which also has more thematic magic traditions.
However, there are several options that I would consider when attempting this for 5e.
(i) Color-Themed Spell Lists: Instead of class-based spell-lists, take the existing spells and create Color-specific spell lists that are shared between classes. So (hypothetically) a Red/Black Cleric may have access to the Red/Black spell lists much as a Red/Black Wizard would. This means that classes should approach shared spell lists differently and do different things and balanced around that conceit. Or maybe a Cleric can only devote themselves to one color, while a Wizard can utilize two colors. The classes would presumably be about how you approach magic (e.g., study, innate, pacts, ideological devotion, etc.) and the spell lists define the Color.
(ii) Class-Tied Colors: Class X is tied to Color 3. This is to say, one could take the approach that certain classes are inherently about certain colors: Wizards are Blue, Warlocks are Black, Clerics are White, Sorcerers/Bards are Red, Druids are Green, etc. This could even tie in with the color-themed spell lists above.
(iii) Color-Appropriate Subclasses: Instead of adjusting the spell lists too drastically, one could instead create Color-appropriate subclasses for each class: e.g., Red Wizard, White Wizard, Red Cleric, Blue Cleric, Green Barbarian, Blue Barbarian, etc. Additional spells and abilities that are appropriate to those class/color combinations could then be doled out. This requires less work than the above.
(iv) Layered On Top: Use something like the Piety system from the Theros book and just add it on top to characters. But instead of "Piety," the characters may have Color Affinities that they are playing into. They may get additional spells, rituals, or benefits from playing into these Color Affinities and those Affinities may change.
From what I gather, the actual sense of being a planeswalker isn't so much now about being a powerful wizard, but by simply being a person who has the planeswalking "spark."
