Spellcasters learn spells based on their paths, but other than a few extra ones at the first and second levels of Priest or Magician, they'll only be learning one new spell per level. Your Power score is the D&D equivalent of your spellcaster level, and it determines how many times between rests you can cast each spell you know, along with the spell level. Basically you're more like a Sorcerer than a Wizard. You know a few spells, and can cast them several times.
On top of that, there are 30 Traditions of spells and you have to learn a Tradition before you can learn any spells from it. You have to spend a spell choice to learn a Tradition, and you learn one 0-level spell (or two if you're a Magician). So you can't just decide to take Fireball when you reach 5th level if you weren't already learning spells from the Fire Tradition.
My greatest worry with this is it will seem like magic doesn't have nearly the versatility that Wizards enjoy in D&D. Players used to being able to find the right spell for any situation will instead be limited to a few spells that are all thematically linked.
There are a few points against the "Wizards can do anything" school of thinking, though. First, it wasn't always that way. Earlier editions had shorter spell lists, fewer spells per day, and encouraged DMs to be very stingy with handing out new spells for a Wizard's spellbook. Also, in every edition there are certain spells which become obvious choices (and personally I hate that). In 3E you were foolish if you didn't have Haste and Dispel Magic prepared for every combat encounter, and the combination of Scry and Teleport at higher levels was a common way to ambush enemies. In 5E, certain spells have routinely caused problems at organized play events. So while Wizards seem to have lots of options, if they all take the same spells there's no real variety.
The magic system does a lot to differentiate between different spellcasters and give them more of a theme. I've gone through lots of builds in my head while reading over magic, and for a character who starts as Magician and takes all spellcasting paths it seems that learning 3 Traditions is the best or most likely option. You could do 2 Traditions but honestly a lot of the lower level attack spells are kind of redundant--do you really need 3 different ways to set someone on fire? If you do 4 Traditions you might be a little under powered at lower levels, but I would only do this if you really want more variety. You'll probably be agonizing over choices between all four every time you can learn a new spell.
Priests might be a little put off by their lack of choices--in D&D Clerics and Druids get access to a large spell list and choose what they want every day. However, a lot of those are false choices also. There are different healing spells for every different affliction. After all of those, you'll probably be picking similar spells every day. Priests have to choose their Traditions from a choice of three, depending on their religion. All religions have Life (healing) as one of the options, but Priests can also heal some with their path abilities if they don't want to spend a spell choice on that.
I'd also be a little forgiving with Tradition choices if the player can come up with a good story reason their character should learn it. Maybe you're the Church's sword of vengeance, so you learn the Battle Tradition, or maybe your Druid worships a thunder god and learns Storm magic. Maybe you're a monk who specializes in elemental Traditions--Avatar: The Last Airbender, anyone?
So while spellcasters in Shadow of the Demon Lord don't have the versatility of most D&D casters, they make up for it with more flavor and more thematically-related spells.
A few other interesting bits about the magic system:
- Some Traditions give you Corruption points for learning them. This includes Necromancy, Curse spells (which Witches are good at), and the Forbidden Tradition, which has awful spells like Hateful Defecation and Ravenous Maggots.
- Any spell can be on a one-time use Incantation (like a scroll), which anybody can attempt to cast. This is a way to add a lot of variety to a campaign.
- There is a Master Path for every Tradition in the core rulebook.
- Spells are split between Attack spells and Utility spells, so every Tradition gives at least some offensive capabilities. I'd also encourage players to be inventive with their Attack spells in non-combat situations, and make ad hoc rulings.
- Traditions are a great way to add flavor to a group in the world--maybe mages of the Ice Tower specialize in Water and Enchantment magic, to freeze their opponents and enslave them, while the goblins of the Lost Woods use Illusion and Teleportation magic to confuse and waylay travelers.
- The Primal Tradition lets you take on bestial traits and summon animals, while the Transformation Tradition lets you take the form of animals, among other things. Primal is better for those who want to boost their combat abilities, Transformation is better for someone who want to stop casting spells and rampage for a bit. Neither aligns with what D&D Druids can do with Wild Shape, so be prepared.
- A Magician with the Battle Tradition can match a Warrior in offense, but is still fragile.
- It still bothers me that none of the religions have Divination as an option for Tradition, given the etymology of the word.
- I don't like to house rule much with a new system, but one thing I'll probably do--give all casters unlimited uses of their 0-level spells. That way they can fire off attacks without resorting to mundane weapons. I'll see how this goes, and adjust as necessary.
- There is one way spellcasters can get more versatility--the Wizard expert path allows three spells in a grimoire that can be cast using spell slots for other spells. I would allow the player to swap out at least one spell per level as they advanced as well.