Yeah, normally, with a deck you go in with an idea or theme choosing 1 or 2 colours, maybe 3 or more for really awkward combo decks, and then refine it . That's kind of what the specialisations would do. If you start out as a blue wizard you can learn all blue coloured spells. If you later reach a level that lets you choose a specialisation you might pick up the ability to learn black magic or you might instead choose a specialisation for blue magic. You might never learn to cast red, green, or white magic and instead focus on boosting your abilities in blue and black.
Secondary colours are also limited in the level of spell you can cast. I think in my current document, that blue wizard who adds black to his repertoire is only able to learn up to 5th level spells, he won't be able to learn up to 9th unless he spends a second specialisation on black magic. I don't know if this would actually be fun in play, but I thought that a planeswalker could either focus on a single colour, gain another 1 or 2 colours and be able to cast up to 9th level spells, or gain the ability to cast all colours but with 4 of them would be limited to 5th (think of it as having plenty of blue mana sources, but only 1 or 2 mana sources of the other colours). I did have a decent green deck that also splashed in white and red a few years back. If I was making that in this system, I'd be a full caster with green as my primary colour and a single pick of red and white as secondary colours.
There is a lot of work that needs to be done on this, I'd actually forgotten that I'd started until I saw your thread. I'm seriously bad at starting but never finishing ideas. I'm always amazed when I manage to complete an entire subclass, that's how bad I can be.