To critique magic systems, you need criteria...and I doubt all readers will share the same criteria (nor is there any reason for them to...)
But to share mine:
1. Whatever the magic system or systems, Story rules--the magic must serve the story, not ruin it.
2. This means that no magic can be unlimited. Unlimited power means there's no conflict (ZAP to the opponent, it's over, so what?)
3. Thus every form of magic operates by some rule system, which the writer needs to know and at least some of which is shared with the reader, so the reader can trust the writer. In a set of psi power stories years ago (which we might now call science fantasy but was then called science fiction) I gave up on the series when the heroine suddenly began popping out a new psi power every time she got into a bind. Deus ex machina is just as annoying with magic as the machina.
4. Magical power can be innate in a person, place, or thing, but the kind of magic inherent in each should be distinct. If, for example, every person, place, or thing that's magical can emit the same kind of light on command...boring.
5. Learned magic should require effort to learn and use. It should also be expensive. Cheap magic; cheap results (something I used in the first fantasy story I ever sold, "Bargains.")
6. The existence of overt magic in a fictional world already stretches the reader's suspension of disbelief...so in more serious works, where it's not supposed to be funny, tone matters. The writer must be able to control the tone of the language to suit the kind of magic and story.
Another consideration is what does the writer mean by magic, and is all the magic magic? Is any extra power (high intelligence, uncommon reaction time, etc.) borderline magic...esp. if you're born with it? My son has absolute pitch--something very few people have--and it certainly amazes people when he can say "Oh, that's a C-sharp minor chord, only the piano's a little flat." In a story, the writer can give non-common powers to characters and not consider that magic, esp. if they aren't human. Humans may call it magic, but to those who possess it, that power may be as normal as our basic senses. In that case, the "magic" is set into the grain of the world-building and won't be "visible" as a magic system. It's just different.
And another--very important to me--is how the writer uses magic in the service of Story. Does the magic introduce additional complications, or just easy ways out? Does the magic feel integral to the world--woven deeply into the fabric of the place, the culture, politics/religion/economics, and the characters, in a way that enriches the story? Or is it a set of standard magic tricks dropped into the story, or even just painted on top, without being fully part of it? Or used merely to make a point...?
Back in the 1920s and 30s, a writer named Thorne Smith wrote some very funny fantasies that were basically spoofs and social commentary. In one, for instance, an annoyed Oriental figurine causes a husband and wife to change bodies...right after he gets her pregnant. In another, statues of classical deities come to life and start cavorting around in New York City, acting like their originals (or, as Homer said their originals acted.) Very different from (most, at least) modern fantasy, but there was magic, and it was limited and had its own logic. Hardly a "system," though.