You sir, have no imagination. What you lump into spellsword alone has many, many unique combinations, such as an illusion thief, death knight (two-handed, heavy armor, conjuration), kensai (dual swords, alteration, no armor), and battlemage (one-handed, destruction, alteration, no armor), just to name a few. Even using the same weapon style, different spell schools can really change the character's feel.
I am talking about functional and gameplay differences that define classes. A Shadowknight (or Deathknight for the WoW kids) is not different from a Warrior because they wear shadowy armor and cast Absorb Health or Raise Skeleton. There is a lot more to creating a defined class. The playstyles in Skyrim are all too similar and there are a total lack of choices. Perks were meant to add specialization so as your character evolves, so does its "class". That is a great concept, but in practice it does not work that way. Characters fall into the categories I posted above.
In your example, a deatknight, a kensai, and a battlemage are all the same. The only difference are what schools of magic your choose to use or armor. The only one that plays even remotely differently is the Battlemage considering you have access to magic as well as melee at the same time. Without swapping weapons, your kensai and deathknight have to swap to cast.
I like dual-casting, but I think it pigeon holed their design team. Ultimately, combined with perks, I think this is why Spell Creation disappeared in Skyrim. Which is sad. There should be more customization, not less.