This, when I started out playing with my Nephews who were 5 and 8 at the time - the younger one played a sorcerer. And it worked, because I went with him trough his spell casting choices and what his character could do ... like, if you have a more or less experienced DM or Player helping the newbie to create a character, most classes a not hard to grasp.
I would imagine, a "simplified" Spellcaster is more akin to a Superhero. Shooting energy blasts from your hands instead of casting spells, creating energy shields, maybe flying ... like a super condensed set of abilities that are magical instead of picking 20+ spells out of a list of 200 spells. Because thats what a Super Hero is: A condesed set of two to four magical (supernatural) abilities.
Super heroes with a bigger set of abilities always end up as someting that looks more like a wizard.
Like - look at the Teen Titans. Robin ... okay, that one is a rogue.
Starfire: Can shoot Energy "Starbolts" (Firebolt? with Force-Energy), can Fly, release all the energy at once (Fireball) ...
Cyborg is more akin to an Artificer/Warforged.
Beast Boy is an at-will Wildshaper.
And then there is raven. A literal Wizard.
A simple Spellcaster would be more akin to Starfire - or Cyclops or any of the other Superheroes whos main abilitiy it is to just shoot some kind of energy/fire/elemental thingy at their enemies.
Mostly agree but think that also gets to the problem with calling fora blaster by way of calling for a "simple arcane caster". No matter how tight and well designed the resulting blaster is, "arcane caster" is too broad of a power set to avoid endless best in class near enough equivalent features getting added on like so many sorlock builds include.
In short, the question along with its resulting goal is too simple and fails to account for the fact that "arcane caster" means buff debuff control utility (sometimes/possibly) magic item crafting and more but phrases things in a way that demands hooks in
all of those . Those hooks result in stuff like all the absurd S tier sorlock)hexadin/bardlock extreme SAD multiclassed over the top shenanigans because the "simple" class was built with the design expectation that it would old ever be played by someone who plays with no thought.
Look at mmo class roles for what the question should be
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Should there be a simple glass cannon blaster? Uhh no... Being an
effective blaster means knowing how to manage your positioning resource burn & "aggro" by learning how and when to shift from phoning in the damage to dumping a truckload of hurt asap.
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Could there be a simple blaster? Sure but it shouldn't be achieved by making the near enough best in class blaster able to operate at full maximum power burn followed by a special recovery method where they can just guilt the group into a looping 5mwd of nova->short rest->repeat.
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Could there be a simple magic item crafter? Not really, that takes too much thought into party/system understanding and it only kinda works with the 5e because they oversimplified magic items and removed their needed churn.
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Should there be a simple magic item crafter? No because that's just a class built around the magic weapon spell until you swap "simple" for something else
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Could there be a simple controller class? probably not because that's usually called a "tank" class and even then a good tank takes some thought and understanding of how to fill the role for their party.
*Should there be a simple buff/debuff class? Probably not, the top tier buff/debuff class is usually also the top tier controller class with good reason. Both sides of that coin are important roles in a group and are almost always appreciated but they aren't always
needed. Knowing when to focus on one the other or neither is not a simple matter and the only way to really make it simple is to stick weaker versions of its abilities into other possibly complex classes as near ribbon level abilities or making the result silly overpowered when played with some thought & understanding.
TLDR; in short the "should their be a simple arcane spellcaster" question should be ignored by designers until it can be phrased in a way that shows the questioner understands what they are asking for enough to be specific enough to convey role/niche understanding while asking. Once that happens then it just becomes something like "is there a need for this not already better filled by a simple guide or pregenfor that class?"