I could think of much better ways to reign in magical power than "and for this part of our adventure, no magic for you".
Even if I agreed depriving someone of their strengths could be interesting, what does a spellcaster have left if they can't even use cantrips? A Cleric could fight in melee, though not as well as a warrior (and I'm still boggled by the idea that there's this random area where even the Gods have no power). Maybe a Bard could manage. Bladesingers and Hexblades/Pact of the Blade Warlocks are screwed. Pure Wizards and Sorcerers? Wow I guess they can go back to throwing darts.
Oh and you know what would be fantastic? Encounter an enemy immune to non-magical weapons in this "anti-magic zone", in which monsters are just fine thanks. Now nobody can do anything!
Anti-Magic Zones sound more like Anti-Player Zones to me.
The reason why magic users don't have to make die rolls to cast spells is pretty basic- they have a limited supply of spells that are more powerful than a dang crossbow (I'll grant that cantrips get better over time, but that's simply because of monster hit point inflation).
Damage dealing spells are, for the most part, pretty inefficient compared to what Fighters, Barbarians, Rangers, and Paladins are doing. Most haven't had their damage increased in a meaningful way since the 80's. Worse, rather than getting better over time, now you have to use higher level spell slots for them.
Just to get 10d6 out of a lightning bolt takes a 5th level spell slot. That's terrible!
Buffs are super nerfed in 5e- most take concentration, and you have better uses for that, so few people are getting buffs, and even Haste has gone from a party buff to something one guy gets, and it has a downside when concentration ends!
So what we're really griping about, are spells that disable enemies and utility spells. Spending one spell slot to disable a group of enemies so it's easier to fight them seems pretty reasonable when you only have so many.
Now the utility stuff, that's where the issues come from, I would think. Especially when it lets the spellcaster affect the narrative in ways a mere skill check cannot.