Arcane was a block mechanic. It didn't require any changes to other sets. It also wasn't a huge success. There wasn't much connecting the different Arcane cards, so it mostly meant "if you want to play with splice or
spiritcraft, you're limited to this small set of often overpriced cards".
The only other spell type, Trap, was also a block mechanic. For the most part, the subtype just tied together the various "cheaper if certain conditions are met" cards, but there were also
two cards that interacted with them specifically. I could see them making more of this type of thing in the future.
What I don't think they will or should do is try to broadly apply spell types to instants and sorceries like they currently do with creature types. There are several key differences between the two.
One is that, when done right, creature types are almost invisible. You can often already guess from the name and art what the creature type should be. Even without knowing about tribal effects, it's clear that a creature card representing a goblin should have the Goblin creature type. With spell types, this is going to be much less clear, especially since none of the existing instants/sorceries were designed with that sort of categorization in mind. Just what type of spell is a
Cathartic Reunion?
Also, creature types are versatile. There are many ways to Goblin, so there are many ways to build a Goblin deck. On the other hand, it seems that most spell types would be closely associated with mechanics. Pyromancy would just largely overlap with "red burn spell", Necromancy would just largely overlap with "black reanimation spell", etc. That would both make it hard to give a set enough of a concentration of a given spell type to allow tribal interactions to happen (there are only so many black reanimation spells a set can have) and hard to build a deck around it. On the other hand, if they're defined more loosely, such that, for example, any card associated with death, vampirism, the undead, or corpses counts as a Necromancy, it would then largely overlap with "black spell" (a bit of an exaggeration, but you get my point).
Another issue is that creatures are just much more interactive. There are all sorts of ways to make tribal creature effects: you can boost their P/T, give them abilities (and there are so many options there), and you can have abilities that trigger when they enter the battlefield, attack/block, deal/are dealt damage, and die. Interactions with instants and sorceries are much more limited. In particular, interactions instants/sorceries can have with other instants/sorceries are
very limited. So it would mostly be an A/B mechanic, where you separately need the spells of a given type and the cards that care about that spell type, making it even harder to build around.
Just consider: in the current Standard, there are 700 cards that mention "creature" in their rules text, but only 15 cards that mention "instant" or "sorcery" (if you exclude the use of those words as timing restrictions, like in embalm's reminder text).