I don't think so, I would rather think that the game is more balanced when the Wizard knows plenty of utility spells and a small selection of combat spells, and then even only some of the combat spells are damage-dealers.
... so the game is most balanced when everyone is playing a
Batman Wizard. Right.
If, however, you have a bunch of players who aren't obsessed with optimising, explicitly don't want to break your game, and just want to play... you'll have a pretty balanced game. And that applies whether you restrict the casters or not.
This applies if and only if the casters aren't being smart or creative with their spells. If you give the most creative and adept players in the group the non-casters you'll probably have a balanced game.
(Or, possibly, if he's bought a scroll or wand. The problem there is that that eats into his limited budget for buying gear - are you sure you wouldn't rather put the money to a better headband of intellect instead?)
The problem with this armchair critique is that there is so much less a caster wants to spend money on than a non-caster, and they get much more bang for their buck when they do.
A wizard needs a Headband of Intellect - the only other items that help the wizard cast in the SRD are metamagic rods, pearls of power, Rings of Wizardry, and the Blessed Book. A fighter on the other hand needs a magic weapon, magic armour, possibly a magic shield, boosters to strength, dex, and possibly con and wis. And that's just getting started.
It's also a very common assumption that the casters get to 'nova' in every encounter. But that's a gamestyle assumption - in a game where casters can't be sure they won't have to fight again, they don't get to just blow through all their spells safely. And that makes a big difference to relative power levels.
Only to some playstyles. The Batman approach is to win the fight with as few spells as possible then sit back and relax watching the mopping up operation.
I think you'd find the game is much easier to balance just by removing scribe scroll and craft wand feats.
That won't fix the problems. But it's a damn good start.
Because, sans your most important stat, most characters look exactly the same. A 28 point buy melee fighter will generally look like:
S16 D14 C15 I10 W10 Ch8 Sure, the odd player will throw a higher int or charisma in there, but generally speaking, most melee fighters will look something like the above. A wizard will most likely be: S8 D16 C14 I16 W10 Ch8.
And this is a specific problem with 3.X (and to a lesser edition 2e). In older editions stats didn't matter much so you could spread them around freely.
With the split save stats 4e has much freer stat placement than 3.X - and has synergy with stats. There are decent builds for the wizard using literally
any stat other than Int as your secondary stat. There are decent builds for a Paragon Thief using Str, Dex, Int, Con, or Cha as your
primary stat. (OK, so you have to be a half elf or revenant for those last two). The Lazy Warlord doesn't even
have a primary stat. The Barbarian has official builds with Dex, Con, and Cha as secondary stats - and my last one was strong enough despite his secondary stat being
Int (and he was a Ritual Caster). And there is no class without at least two viable secondary stats.
This is what balance means - almost all concepts are viable unless obviously not.
There's never a strong charismatic fighter or a strong wizard or any variation.
I've seen both those in 4e.